# How do you solve for t K= H - Ca^t?

Jan 28, 2016

$t = {\log}_{a} \left(\frac{H - K}{C}\right)$

#### Explanation:

First, isolate the term with $t$.

$K - H = - C {a}^{t}$

Divide by $- C$.

$\frac{H - K}{C} = {a}^{t}$

To undo an exponential function like ${a}^{t}$ in order to solve for $t$, we will have to use a logarithm. Logarithms and exponential functions are inverses.

${\log}_{a} \left(\frac{H - K}{C}\right) = {\log}_{a} \left({a}^{t}\right)$

$t = {\log}_{a} \left(\frac{H - K}{C}\right)$