Solve for x 4(2.5)^(2x)=4

$4 {(2.5)}^{2 x} = 4$

Divide each term in $(4 \cdot {2.5}^{2 x}) = 4$ by $4$ and simplify.

Divide each term in $(4 \cdot {2.5}^{2 x}) = 4$ by $4$ .

$\frac{(4 \cdot {2.5}^{2 x})}{4} = \frac{4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \cdot {2.5}^{2 x}}{4} = \frac{4}{4}$

Divide ${2.5}^{2 x}$ by $1$ .

${2.5}^{2 x} = \frac{4}{4}$

Simplify the right side.

Divide $4$ by $4$ .

${2.5}^{2 x} = 1$

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

$\ln ({2.5}^{2 x}) = \ln (1)$

Expand $\ln ({2.5}^{2 x})$ by moving $2 x$ outside the logarithm.

$2 x \ln (2.5) = \ln (1)$

Simplify the right side.

The natural logarithm of $1$ is $0$ .

$2 x \ln (2.5) = 0$

Divide each term in $2 x \ln (2.5) = 0$ by $2 \ln (2.5)$ and simplify.

Divide each term in $2 x \ln (2.5) = 0$ by $2 \ln (2.5)$ .

$\frac{2 x \ln (2.5)}{2 \ln (2.5)} = \frac{0}{2 \ln (2.5)}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x \ln (2.5)}{2 \ln (2.5)} = \frac{0}{2 \ln (2.5)}$

Rewrite the expression.

$\frac{x \ln (2.5)}{\ln (2.5)} = \frac{0}{2 \ln (2.5)}$

Cancel the common factor of $\ln (2.5)$ .

Cancel the common factor.

$\frac{x \ln (2.5)}{\ln (2.5)} = \frac{0}{2 \ln (2.5)}$

Divide $x$ by $1$ .

$x = \frac{0}{2 \ln (2.5)}$

Simplify the right side.

Cancel the common factor of $0$ and $2$ .

Factor $2$ out of $0$ .

$x = \frac{2 (0)}{2 \ln (2.5)}$

Cancel the common factors.

Factor $2$ out of $2 \ln (2.5)$ .

$x = \frac{2 (0)}{2 (\ln (2.5))}$

Cancel the common factor.

$x = \frac{2 \cdot 0}{2 \ln (2.5)}$

Rewrite the expression.

$x = \frac{0}{\ln (2.5)}$

Divide $0$ by $\ln (2.5)$ .

$x = 0$

Solve for x 4(2.5)^(2x)=4

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