Question

Log 4 base √2
(please show working)

Answer 1

Solution :-

$\text{Let } \tt log_{ \sqrt{2} }4 = x$

Writing it in exponential form

$\implies \tt (\sqrt{2})^{x} = 4$

[ Because, if log N to the base a = x then a^x = N ]

It can be written as

$\implies \tt \bigg(2^{ \dfrac{1}{2} } \bigg)^{x} = 4$

$\implies \tt 2^{ \dfrac{x}{2} } = 4$

[ Because (a^m)^n = a^(mn) ]

$\implies \tt 2^{ \dfrac{x}{2} } = {2}^{2}$

Since bases are equal we can equate powers

$\implies \tt \dfrac{x}{2} = 2$

$\implies \tt x = 4$

$\implies \tt log_{ \sqrt{2} }4 = 4$

Therefore the value of log 4 to the base √2 is 4.