Find the Exact Value log base 2 of 1/32

$\log_{2} (\frac{1}{32})$

Step 1

Rewrite as an equation.

$\log_{2} (\frac{1}{32}) = x$

Step 2

Rewrite $\log_{2} (\frac{1}{32}) = x$ 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 $b^{y} = x$ .

$2^{x} = \frac{1}{32}$

Step 3

Create equivalent expressions in the equation that all have equal bases.

$2^{x} = 2^{- 5}$

Step 4

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

$x = - 5$

Step 5

The variable $x$ is equal to $- 5$ .

$- 5$

Find the Exact Value log base 2 of 1/32

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