Solve for x 5^(x+1)-3/25=2.5^x

$5^{x + 1} - \frac{3}{25} = {2.5}^{x}$

Simplify $5^{x + 1} - \frac{3}{25}$ .

To write $5^{x + 1}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$5^{x + 1} \cdot \frac{25}{25} - \frac{3}{25} = {2.5}^{x}$

Combine $5^{x + 1}$ and $\frac{25}{25}$ .

$\frac{5^{x + 1} \cdot 25}{25} - \frac{3}{25} = {2.5}^{x}$

Combine the numerators over the common denominator.

$\frac{5^{x + 1} \cdot 25 - 3}{25} = {2.5}^{x}$

Multiply $5^{x + 1} \cdot 25$ .

Rewrite $25$ as $5^{2}$ .

$\frac{5^{x + 1} \cdot 5^{2} - 3}{25} = {2.5}^{x}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5^{x + 1 + 2} - 3}{25} = {2.5}^{x}$

Add $1$ and $2$ .

$\frac{5^{x + 3} - 3}{25} = {2.5}^{x}$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 1.68063721$