Solve for x log base 7 of x=-2

$\log_{7} (x) = - 2$

Step 1

Rewrite $\log_{7} (x) = - 2$ 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 $b^{y} = x$ .

$7^{- 2} = x$

Step 2

Solve for $x$ .

Rewrite the equation as $x = 7^{- 2}$ .

$x = 7^{- 2}$

Simplify $7^{- 2}$ .

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

$x = \frac{1}{7^{2}}$

Raise $7$ to the power of $2$ .

$x = \frac{1}{49}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{49}$

Decimal Form:

$x = 0.02040816 \dots$

Solve for x log base 7 of x=-2

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