Evaluate log base 3 of (1/27)^4

$\log_{3} ({(\frac{1}{27})}^{4})$

Apply the product rule to $\frac{1}{27}$ .

$\log_{3} (\frac{1^{4}}{27^{4}})$

One to any power is one.

$\log_{3} (\frac{1}{27^{4}})$

Raise $27$ to the power of $4$ .

$\log_{3} (\frac{1}{531441})$

Logarithm base $3$ of $\frac{1}{531441}$ is $- 12$ .

Rewrite as an equation.

$\log_{3} (\frac{1}{531441}) = x$

Rewrite $\log_{3} (\frac{1}{531441}) = x$ 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 $b^{y} = x$ .

$3^{x} = \frac{1}{531441}$

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

$3^{x} = 3^{- 12}$

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

$x = - 12$

The variable $x$ is equal to $- 12$ .

$- 12$

Evaluate log base 3 of (1/27)^4

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