Evaluate log base 4 of 64

$\log_{4} (64)$

Rewrite as an equation.

$\log_{4} (64) = x$

Rewrite $\log_{4} (64) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$4^{x} = 64$

Create expressions in the equation that all have equal bases.

${(2^{2})}^{x} = 2^{6}$

Rewrite ${(2^{2})}^{x}$ as $2^{2 x}$ .

$2^{2 x} = 2^{6}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 x = 6$

Solve for $x$ .

$x = 3$

The variable $x$ is equal to $3$ .

$3$

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