Question

solve for a positive value of x.\\(\log_{4}(64) = x\\)

Explanation:

Step1: Recall logarithm definition

The logarithmic equation $\log_{b}(a) = x$ is equivalent to $b^{x}=a$. So for $\log_{4}(64)=x$, we can rewrite it as $4^{x}=64$.

Step2: Express 64 as a power of 4

We know that $4^{3}=4\times4\times4 = 64$. So we have $4^{x}=4^{3}$.

Step3: Solve for x

Since the bases are the same and the exponential function is one - to - one (if $b^{m}=b^{n}$, then $m = n$ for $b>0,b
eq1$), we can conclude that $x = 3$.

Answer:

3