# How do you solve log_m 2=4?

Sep 11, 2016

$m = \sqrt[4]{2} = {2}^{\frac{1}{4}}$

#### Explanation:

I made the assumption that the question as $\log - m + 2 = 4$ was meant to be ${\log}_{m} 2 = 4$?

Log form and index from are interchangeable. It is often easier to understand and do the question by changing the format.

${\log}_{a} b = c \text{ "hArr " } {a}^{c} = b$

${\log}_{m} 2 = 4 = {m}^{4} = 2$

${\sqrt[4]{m}}^{4} = \sqrt[4]{2}$

$m = \sqrt[4]{2} = {2}^{\frac{1}{4}}$

While there are always 2 possible roots, the negative root does not work, leaving us with only one possible solution for m.

Thank you, Tazwar Sikder for the insight. :)