Algebra Examples

5^{x} = 52

$5^{x} = 52$

Step 1

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

\ln (5^{x}) = \ln (52)

$\ln (5^{x}) = \ln (52)$

Step 2

Expand

\ln (5^{x})

$\ln (5^{x})$ by moving

x

$x$ outside the logarithm.

x \ln (5) = \ln (52)

$x \ln (5) = \ln (52)$

Step 3

Divide each term in

x \ln (5) = \ln (52)

$x \ln (5) = \ln (52)$ by

\ln (5)

$\ln (5)$ and simplify.

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Step 3.1

Divide each term in

x \ln (5) = \ln (52)

$x \ln (5) = \ln (52)$ by

\ln (5)

$\ln (5)$ .

\frac{x \ln (5)}{\ln (5)} = \frac{\ln (52)}{\ln (5)}

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (52)}{\ln (5)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

\ln (5)

$\ln (5)$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{x \ln (5)}{\ln (5)} = \frac{\ln (52)}{\ln (5)}

$\frac{x \ln (5)}{\ln (5)} = \frac{\ln (52)}{\ln (5)}$

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (52)}{\ln (5)}