Evaluate e^(5x-2)=6

$e^{5 x - 2} = 6$

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

$\ln (e^{5 x - 2}) = \ln (6)$

Expand the left side.

Expand $\ln (e^{5 x - 2})$ by moving $5 x - 2$ outside the logarithm.

$(5 x - 2) \ln (e) = \ln (6)$

The natural logarithm of $e$ is $1$ .

$(5 x - 2) \cdot 1 = \ln (6)$

Multiply $5 x - 2$ by $1$ .

$5 x - 2 = \ln (6)$

Add $2$ to both sides of the equation.

$5 x = \ln (6) + 2$

Divide each term in $5 x = \ln (6) + 2$ by $5$ and simplify.

Divide each term in $5 x = \ln (6) + 2$ by $5$ .

$\frac{5 x}{5} = \frac{\ln (6)}{5} + \frac{2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{\ln (6)}{5} + \frac{2}{5}$

Divide $x$ by $1$ .

$x = \frac{\ln (6)}{5} + \frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (6)}{5} + \frac{2}{5}$

Decimal Form:

$x = 0.75835189 \dots$