Algebra Examples

$5^{x} = 2$

Step 1

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

$\ln (5^{x}) = \ln (2)$

Step 2

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

$x \ln (5) = \ln (2)$

Step 3

Divide each term in $x \ln (5) = \ln (2)$ by $\ln (5)$ and simplify.

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Step 3.1

Divide each term in $x \ln (5) = \ln (2)$ by $\ln (5)$ .

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (2)}{\ln (5)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (2)}{\ln (5)}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (2)}{\ln (5)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (2)}{\ln (5)}$

Decimal Form:

$x = 0.43067655 \dots$