Algebra Examples

$7^{x} = 12$

Step 1

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

$\ln (7^{x}) = \ln (12)$

Step 2

Expand

$\ln (7^{x})$ by moving

$x$ outside the logarithm.

$x \ln (7) = \ln (12)$

Step 3

Divide each term in

$x \ln (7) = \ln (12)$ by

$\ln (7)$ and simplify.

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Step 3.1

Divide each term in

$x \ln (7) = \ln (12)$ by

$\ln (7)$ .

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (12)}{\ln (7)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$\ln (7)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (12)}{\ln (7)}$

Step 3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{\ln (12)}{\ln (7)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (12)}{\ln (7)}$

Decimal Form:

$x = 1.27698940 \dots$