How do you write the equation log_7 (1/2401)=-4 into exponential form?

Dec 20, 2016

${7}^{-} 4 = \frac{1}{2401}$

Explanation:

Write ${\log}_{7} \left(\frac{1}{2401}\right) = - 4$ as an exponential.

Use the rule ${\log}_{b} x = a \textcolor{w h i t e}{a a} \implies \textcolor{w h i t e}{a a} x = {b}^{a}$

${\log}_{7} \left(\frac{1}{2401}\right) = - 4 \textcolor{w h i t e}{a a} \implies \textcolor{w h i t e}{a a} {7}^{-} 4 = \frac{1}{2401}$

Note that the $7$ is the base of the log and the base of the exponential. And, the "answer" to a log equation is the exponent of the exponential.