Pre-Algebra Examples

${9.5}^{x} = 89$

Step 1

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

$\ln ({9.5}^{x}) = \ln (89)$

Step 2

Expand $\ln ({9.5}^{x})$ by moving $x$ outside the logarithm.

$x \ln (9.5) = \ln (89)$

Step 3

Divide each term in $x \ln (9.5) = \ln (89)$ by $\ln (9.5)$ and simplify.

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Step 3.1

Divide each term in $x \ln (9.5) = \ln (89)$ by $\ln (9.5)$ .

$\frac{x \ln (9.5)}{\ln (9.5)} = \frac{\ln (89)}{\ln (9.5)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\ln (9.5)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \ln (9.5)}{\ln (9.5)} = \frac{\ln (89)}{\ln (9.5)}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (89)}{\ln (9.5)}$