Question

If log10(log2(log4x) = 0 find the value of x

Answer 1

Given problem is

$\log_{10}(\log_{2}(\log_{4}(x)))=0$

Now we have to find the value of x. In order to find value of x, we need to isolate x which can be done by converting logarithmic equation into exponential equation using formula:

$\log_{b}(a)=c \Rightarrow b^c=a$

In this formula, base (b) remains fixed at it's position while other values a and c switch. So applying this formula on given problem, we get:

$10^0=\log_{2}(\log_{4}(x))$

$1=\log_{2}(\log_{4}(x))$

$\log_{2}(\log_{4}(x))=1$

Apply above formula again.

$2^1=\log_{4}(x)$

$2=\log_{4}(x)$

$\log_{4}(x)=2$

Apply above formula again.

$4^2=x$

16=x

Hence final answer is x=16.