Solve for X log base 3 of X=-3

$\log_{3} (X) = - 3$

Step 1

Rewrite $\log_{3} (X) = - 3$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$3^{- 3} = X$

Step 2

Solve for $X$ .

Rewrite the equation as $X = 3^{- 3}$ .

$X = 3^{- 3}$

Simplify $3^{- 3}$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$X = \frac{1}{3^{3}}$

Raise $3$ to the power of $3$ .

$X = \frac{1}{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$X = \frac{1}{27}$

Decimal Form:

$X = 0.\overline{037}$

Solve for X log base 3 of X=-3

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