Algebra Examples

8^{x} = 12

$8^{x} = 12$

Step 1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

\ln (8^{x}) = \ln (12)

$\ln (8^{x}) = \ln (12)$

Step 2

Expand

\ln (8^{x})

$\ln (8^{x})$ by moving

x

$x$ outside the logarithm.

x \ln (8) = \ln (12)

$x \ln (8) = \ln (12)$

Step 3

Divide each term in

x \ln (8) = \ln (12)

$x \ln (8) = \ln (12)$ by

\ln (8)

$\ln (8)$ and simplify.

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Step 3.1

Divide each term in

x \ln (8) = \ln (12)

$x \ln (8) = \ln (12)$ by

\ln (8)

$\ln (8)$ .

\frac{x \ln (8)}{\ln (8)} = \frac{\ln (12)}{\ln (8)}

$\frac{x \ln (8)}{\ln (8)} = \frac{\ln (12)}{\ln (8)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

\ln (8)

$\ln (8)$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{x \ln (8)}{\ln (8)} = \frac{\ln (12)}{\ln (8)}

$\frac{x \ln (8)}{\ln (8)} = \frac{\ln (12)}{\ln (8)}$

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (12)}{\ln (8)}