Solve for x 2(5^x)-1=15

$2 (5^{x}) - 1 = 15$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$2 \cdot 5^{x} = 15 + 1$

Add $15$ and $1$ .

$2 \cdot 5^{x} = 16$

Step 2

Divide each term in $(2 \cdot 5^{x}) = 16$ by $2$ and simplify.

Divide each term in $(2 \cdot 5^{x}) = 16$ by $2$ .

$\frac{(2 \cdot 5^{x})}{2} = \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 5^{x}}{2} = \frac{16}{2}$

Divide $5^{x}$ by $1$ .

$5^{x} = \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

$5^{x} = 8$

Step 3

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

$\ln (5^{x}) = \ln (8)$

Step 4

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

$x \ln (5) = \ln (8)$

Step 5

Divide each term in $x \ln (5) = \ln (8)$ by $\ln (5)$ and simplify.

Divide each term in $x \ln (5) = \ln (8)$ by $\ln (5)$ .

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (8)}{\ln (5)}$

Simplify the left side.

Cancel the common factor of $\ln (5)$ .

Cancel the common factor.

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (8)}{\ln (5)}$

Divide $x$ by $1$ .

$x = \frac{\ln (8)}{\ln (5)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (8)}{\ln (5)}$

Decimal Form:

$x = 1.29202967 \dots$