Solve for x 7^x=6

$7^{x} = 6$

Step 1

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

$\ln (7^{x}) = \ln (6)$

Step 2

Expand $\ln (7^{x})$ by moving $x$ outside the logarithm.

$x \ln (7) = \ln (6)$

Step 3

Divide each term in $x \ln (7) = \ln (6)$ by $\ln (7)$ and simplify.

Divide each term in $x \ln (7) = \ln (6)$ by $\ln (7)$ .

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (6)}{\ln (7)}$

Simplify the left side.

Cancel the common factor of $\ln (7)$ .

Cancel the common factor.

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (6)}{\ln (7)}$

Divide $x$ by $1$ .

$x = \frac{\ln (6)}{\ln (7)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (6)}{\ln (7)}$

Decimal Form:

$x = 0.92078222 \dots$