Simplify/Condense log base 4 of 1/16

$\log_{4} (\frac{1}{16})$

Rewrite as an equation.

$\log_{4} (\frac{1}{16}) = x$

Rewrite $\log_{4} (\frac{1}{16}) = x$ 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 $b^{y} = x$ .

$4^{x} = \frac{1}{16}$

Create expressions in the equation that all have equal bases.

${(2^{2})}^{x} = 2^{- 4}$

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

$2^{2 x} = 2^{- 4}$

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

$2 x = - 4$

Solve for $x$ .

$x = - 2$

The variable $x$ is equal to $- 2$ .

$- 2$

Simplify/Condense log base 4 of 1/16

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