Drag matching base
Can we make the bases match? Replace {{state.targetVal}} with a power of {{state.baseA}}.
=
{{ state.targetVal }}
Tap exponents to equate
The bases are both {{state.baseA}}. That means their exponents must be equal!
{{ formatLinear(state.m, state.c) }}
{{ state.baseA }}
=
{{ state.targetPower }}
{{ state.baseA }}
{{ formatLinear(state.m, state.c) }} = {{ state.targetPower }}
We've transformed it into a simple linear equation!
Adjust slider to solve
Find the value of x that balances the equation.
{{ state.m }}
({{ state.xGuess }})
{{ state.c > 0 ? '+' : '-' }} {{ Math.abs(state.c) }}
=
{{ state.targetPower }}
Result: {{ currentLHS }}
-5
0
5
10
Drag ln to equation
Tap x to drop
Tap ln to isolate
Solved!
Can we write {{state.valLog}} as a power of {{state.baseLog}}? No! Apply the natural logarithm (ln).
Power Rule! The exponent can come down to the front.
Now divide both sides to isolate x!
Great job! This is the exact answer.
ln({{ state.baseLog }}
x
) = ln({{ state.valLog }})
x
ln({{ state.baseLog }})
= ln({{ state.valLog }})
ln
Slide to find intersection
Let's see the exact answer visually! Find where the curves cross.
x = {{ state.graphX.toFixed(2) }}
|
y = {{ Math.pow(state.baseLog, state.graphX).toFixed(2) }}