Solve for x 1-9^x=0.25

$1 - 9^{x} = 0.25$

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

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Subtract $1$ from both sides of the equation.

$- 9^{x} = 0.25 - 1$

Subtract $1$ from $0.25$ .

$- 9^{x} = - 0.75$

Multiply each term in $- 9^{x} = - 0.75$ by $- 1$

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Multiply each term in $- 9^{x} = - 0.75$ by $- 1$ .

$(- 9^{x}) \cdot - 1 = (- 0.75) \cdot - 1$

Multiply $(- 9^{x}) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 \cdot 9^{x} = (- 0.75) \cdot - 1$

Multiply $9^{x}$ by $1$ .

$9^{x} = (- 0.75) \cdot - 1$

Multiply $- 0.75$ by $- 1$ .

$9^{x} = 0.75$

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

$\ln (9^{x}) = \ln (0.75)$

Expand $\ln (9^{x})$ by moving $x$ outside the logarithm.

$x \ln (9) = \ln (0.75)$

Divide each term by $\ln (9)$ and simplify.

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Divide each term in $x \ln (9) = \ln (0.75)$ by $\ln (9)$ .

$\frac{x \ln (9)}{\ln (9)} = \frac{\ln (0.75)}{\ln (9)}$

Cancel the common factor of $\ln (9)$ .

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Cancel the common factor.

$\frac{x \ln (9)}{\ln (9)} = \frac{\ln (0.75)}{\ln (9)}$

Divide $x$ by $1$ .

$x = \frac{\ln (0.75)}{\ln (9)}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (0.75)}{\ln (9)}$

Decimal Form:

$x = - 0.13092975 \dots$

Solve for x 1-9^x=0.25

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