Question

Logrithm of a number to the base √2 is 2 what will be the logrithm of that number to the base 2√2​

Answer 1

Answer:

The answer is $\dfrac{2}{3}$

Step-by-step explanation:

Let x be the number

Given  $\log_{\sqrt 2}x=2$

          $\Rightarrow x=(\sqrt 2)^2=2$

• Since $\log_ax=y\Rightarrow x=a^y$

Thus $\log_{2\sqrt 2}x=\log_{2^{(1+\frac{1}{2})}}(2)=\log_{2^{\frac{3}{2}}}(2)=\dfrac{1}{\frac{3}{2}}\log_22=\frac{2}{3}(1)=\frac{2}{3}$

• Since $\log_{a^n}b=\frac{1}{n}\log_ab$ and $\log_aa=1$