# How do you solve  2a^(t/3)=5?

Dec 13, 2015

Use a logarithm to remove $t$ from the exponent and find that
$t = \frac{3 \ln \left(\frac{5}{2}\right)}{\ln} \left(a\right)$

#### Explanation:

Using the property of logarithms that
$\ln \left({a}^{x}\right) = x \ln \left(a\right)$
we have

$2 {a}^{\frac{t}{3}} = 5$

$\implies {a}^{\frac{t}{3}} = \frac{5}{2}$

$\implies \ln \left({a}^{\frac{t}{3}}\right) = \ln \left(\frac{5}{2}\right)$

$\implies \frac{t}{3} \ln \left(a\right) = \ln \left(\frac{5}{2}\right)$

$\implies t = \frac{3 \ln \left(\frac{5}{2}\right)}{\ln} \left(a\right)$