Solve for x 5x+12^x=5x+7

$5 x + 12^{x} = 5 x + 7$

Move all terms containing $x$ to the left side of the equation.

Subtract $5 x$ from both sides of the equation.

$5 x + 12^{x} - 5 x = 7$

Combine the opposite terms in $5 x + 12^{x} - 5 x$ .

Subtract $5 x$ from $5 x$ .

$0 + 12^{x} = 7$

Add $0$ and $12^{x}$ .

$12^{x} = 7$

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

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

Expand $\ln (12^{x})$ by moving $x$ outside the logarithm.

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

Divide each term in $x \ln (12) = \ln (7)$ by $\ln (12)$ and simplify.

Divide each term in $x \ln (12) = \ln (7)$ by $\ln (12)$ .

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

Simplify the left side.

Cancel the common factor of $\ln (12)$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.78309185 \dots$