Solve for x log base (4/3) of x=-2

$\log_{(\frac{4}{3})} (x) = - 2$

Rewrite $\log_{\frac{4}{3}} (x) = - 2$ 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 $b^{y} = x$ .

${(\frac{4}{3})}^{- 2} = x$

Solve for $x$ .

Rewrite the equation as $x = {(\frac{4}{3})}^{- 2}$ .

$x = {(\frac{4}{3})}^{- 2}$

Simplify ${(\frac{4}{3})}^{- 2}$ .

Change the sign of the exponent by rewriting the base as its reciprocal.

$x = {(\frac{3}{4})}^{2}$

Apply the product rule to $\frac{3}{4}$ .

$x = \frac{3^{2}}{4^{2}}$

Raise $3$ to the power of $2$ .

$x = \frac{9}{4^{2}}$

Raise $4$ to the power of $2$ .

$x = \frac{9}{16}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{16}$

Decimal Form:

$x = 0.5625$

Solve for x log base (4/3) of x=-2

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