Solve for y log base 4 of 1/8=y

$\log_{4} (\frac{1}{8}) = y$

Rewrite the equation as $y = \log_{4} (\frac{1}{8})$ .

$y = \log_{4} (\frac{1}{8})$

Logarithm base $4$ of $\frac{1}{8}$ is $- \frac{3}{2}$ .

Rewrite as an equation.

$y = \log_{4} (\frac{1}{8}) = x$

Rewrite $\log_{4} (\frac{1}{8}) = x$ 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 $b^{y} = x$ .

$y = 4^{x} = \frac{1}{8}$

Create expressions in the equation that all have equal bases.

$y = {(2^{2})}^{x} = 2^{- 3}$

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

$y = 2^{2 x} = 2^{- 3}$

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

$y = 2 x = - 3$

Solve for $x$ .

$y = x = - \frac{3}{2}$

The variable $x$ is equal to $- \frac{3}{2}$ .

$y = - \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{3}{2}$

Decimal Form:

$y = - 1.5$

Mixed Number Form:

$y = - 1 \frac{1}{2}$

Solve for y log base 4 of 1/8=y

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