# How do you write the equation 2401^(1/4)=7 in logarithmic form?

Oct 25, 2016

I tried this:

#### Explanation:

I would try by taking the log in base $7$ of both sides:
${\log}_{7} {\left(2401\right)}^{\frac{1}{4}} = {\log}_{7} \left(7\right)$
using a property of logs (exponent of the argument) and the definition of log we get:
$\frac{1}{4} {\log}_{7} \left(2401\right) = 1$
${\log}_{7} \left(2401\right) = 1 \cdot 4$
${\log}_{7} \left(2401\right) = 4$

and so, using the definition of log we have that indeed:
$2401 = {7}^{4}$