Answer
Sample answer:
We need logarithms to solve some exponential equations (equations where the variable is in the exponent).
Work Step by Step
We need logarithms to solve exponential equations (equations where the variable is in the exponent).
For example, to find $t$ in $200=112(0.025)^{4t}$, we divide with $112$:
$200/112=(0.025)^{4t}$
We need to take the logarithm of both sides, using the rule
$\log_{b}\left(x^{r}\right)=r\log_{b}x$
This allows for $t$ to exit the exponent and the equation becomes:
$\log(200/112)=4t\cdot\log(0.025)$
We finish by dividing both sides with $4\log(0.025)$, which will allow us to solve for $t$.
