Exercise algebra.manipulation.logarithmic.equation
Description
solve logarithmic equation algebraically
Strategy
<label name="logarithmicequation">
<sequence>
<orelse>
<rule name="algebra.manipulation.logarithmic.logarithm"/>
<succeed/>
</orelse>
<orelse>
<sequence>
<rule name="check"/>
<rule name="algebra.equations.linear.flip"/>
</sequence>
<succeed/>
</orelse>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.manipulation.exponents.equation.nth-root"/>
<rule name="arithmetic.operation.rational.power"/>
<rule name="algebra.manipulation.exponents.calc-power.plus"/>
<rule name="algebra.manipulation.exponents.calc-power.minus"/>
<rule name="algebra.manipulation.exponents.root"/>
<rule name="algebra.manipulation.exponents.power-ratio"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
<label name="quadraticequationstrategy">
<let>
<decl var="4">
<orelse>
<sequence>
<orelse>
<let>
<decl var="1">
<choice>
<label name="generalform">
<choice>
<rule name="algebra.equations.quadratic.common-factor"/>
<rule name="algebra.equations.quadratic.no-lin"/>
<rule name="algebra.equations.quadratic.simpler-poly"/>
<rule name="algebra.equations.quadratic.scale" removed="true"/>
<rule name="algebra.equations.quadratic.nice-factors"/>
<rule name="algebra.equations.coverup.power"/>
</choice>
</label>
<label name="abcform">
<rule name="algebra.equations.quadratic.abc"/>
</label>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="1">
<choice>
<label name="zeroform">
<rule name="algebra.equations.quadratic.product-zero"/>
</label>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="1">
<choice>
<label name="constantform">
<choice>
<rule name="algebra.equations.coverup.onevar.plus"/>
<rule name="algebra.equations.coverup.onevar.minus-left"/>
<rule name="algebra.equations.coverup.onevar.minus-right"/>
<rule name="algebra.equations.coverup.times"/>
<rule name="algebra.equations.coverup.negate"/>
<rule name="algebra.equations.coverup.numerator"/>
<rule name="algebra.equations.quadratic.square-both"/>
<rule name="algebra.equations.quadratic.left-square"/>
</choice>
</label>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<choice>
<label name="squarerootsimplification">
<rule name="algebra.equations.quadratic.simpler-sqrt"/>
</label>
<label name="approximateresult" removed="true">
<label name="algebra.equations.quadratic.approx" collapsed="true">
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.approx"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.approx"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
</label>
</label>
</choice>
<label name="topform">
<orelse>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.cancel"/>
<rule name="algebra.equations.quadratic.same-factor"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<choice>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.same-con-factor"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<label name="algebra.equations.linear.merge" collapsed="true">
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.linear.merge"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.linear.merge"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
</label>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.distr-square"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
<label name="algebra.equations.linear.distr-times" collapsed="true">
<sequence>
<let>
<decl var="1">
<orelse>
<rule name="algebra.equations.linear.distr-times"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</orelse>
</decl>
<var var="1"/>
</let>
<let>
<decl var="3">
<orelse>
<sequence>
<let>
<decl var="1">
<orelse>
<rule name="algebra.equations.linear.distr-times"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</orelse>
</decl>
<var var="1"/>
</let>
<var var="3"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="3"/>
</let>
</sequence>
</label>
<rule name="algebra.equations.quadratic.distr-div"/>
<let>
<decl var="1">
<choice>
<sequence>
<rule name="check"/>
<rule name="algebra.equations.linear.flip"/>
</sequence>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
</choice>
<let>
<decl var="1">
<choice>
<rule name="algebra.equations.quadratic.move-left"/>
<rule name="algebra.equations.quadratic.prepare-split" removed="true"/>
<sequence>
<rule name="navigator.down"/>
<succeed/>
<let>
<decl var="2">
<choice>
<var var="1"/>
<sequence>
<rule name="navigator.right"/>
<succeed/>
<var var="2"/>
</sequence>
</choice>
</decl>
<var var="2"/>
</let>
<orelse>
<rule name="navigator.up"/>
<succeed/>
</orelse>
</sequence>
</choice>
</decl>
<var var="1"/>
</let>
</orelse>
</label>
</orelse>
<var var="4"/>
</sequence>
<succeed/>
</orelse>
</decl>
<var var="4"/>
</let>
</label>
</sequence>
</label>Locations
| Location | Label |
| [] | logarithmicequation |
| [0] | ...algebra.manipulation.logarithmic.logarithm |
| [1] | ...algebra.equations.linear.flip |
| [2] | ...algebra.manipulation.exponents.equation.nth-root |
| [3] | ...arithmetic.operation.rational.power |
| [4] | ...algebra.manipulation.exponents.calc-power.plus |
| [5] | ...algebra.manipulation.exponents.calc-power.minus |
| [6] | ...algebra.manipulation.exponents.root |
| [7] | ...algebra.manipulation.exponents.power-ratio |
| [8] | ...quadraticequationstrategy |
| [0,8] | ......generalform |
| [0,0,8] | .........algebra.equations.quadratic.common-factor |
| [1,0,8] | .........algebra.equations.quadratic.no-lin |
| [2,0,8] | .........algebra.equations.quadratic.simpler-poly |
| [3,0,8] | .........algebra.equations.quadratic.scale |
| [4,0,8] | .........algebra.equations.quadratic.nice-factors |
| [5,0,8] | .........algebra.equations.coverup.power |
| [1,8] | ......abcform |
| [0,1,8] | .........algebra.equations.quadratic.abc |
| [2,8] | ......zeroform |
| [0,2,8] | .........algebra.equations.quadratic.product-zero |
| [3,8] | ......constantform |
| [0,3,8] | .........algebra.equations.coverup.onevar.plus |
| [1,3,8] | .........algebra.equations.coverup.onevar.minus-left |
| [2,3,8] | .........algebra.equations.coverup.onevar.minus-right |
| [3,3,8] | .........algebra.equations.coverup.times |
| [4,3,8] | .........algebra.equations.coverup.negate |
| [5,3,8] | .........algebra.equations.coverup.numerator |
| [6,3,8] | .........algebra.equations.quadratic.square-both |
| [7,3,8] | .........algebra.equations.quadratic.left-square |
| [4,8] | ......squarerootsimplification |
| [0,4,8] | .........algebra.equations.quadratic.simpler-sqrt |
| [5,8] | ......approximateresult |
| [0,5,8] | .........algebra.equations.quadratic.approx |
| [0,0,5,8] | ............algebra.equations.quadratic.approx |
| [1,0,5,8] | ............algebra.equations.quadratic.approx |
| [6,8] | ......topform |
| [0,6,8] | .........algebra.equations.quadratic.cancel |
| [1,6,8] | .........algebra.equations.quadratic.same-factor |
| [2,6,8] | .........algebra.equations.quadratic.same-con-factor |
| [3,6,8] | .........algebra.equations.linear.merge |
| [0,3,6,8] | ............algebra.equations.linear.merge |
| [1,3,6,8] | ............algebra.equations.linear.merge |
| [4,6,8] | .........algebra.equations.quadratic.distr-square |
| [5,6,8] | .........algebra.equations.linear.distr-times |
| [0,5,6,8] | ............algebra.equations.linear.distr-times |
| [1,5,6,8] | ............algebra.equations.linear.distr-times |
| [6,6,8] | .........algebra.equations.quadratic.distr-div |
| [7,6,8] | .........algebra.equations.linear.flip |
| [8,6,8] | .........algebra.equations.quadratic.move-left |
| [9,6,8] | .........algebra.equations.quadratic.prepare-split |