Algebra Examples

4^{x} = 26

$4^{x} = 26$

Step 1

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

\ln (4^{x}) = \ln (26)

$\ln (4^{x}) = \ln (26)$

Step 2

Expand

\ln (4^{x})

$\ln (4^{x})$ by moving

x

$x$ outside the logarithm.

x \ln (4) = \ln (26)

$x \ln (4) = \ln (26)$

Step 3

Divide each term in

x \ln (4) = \ln (26)

$x \ln (4) = \ln (26)$ by

\ln (4)

$\ln (4)$ and simplify.

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Step 3.1

Divide each term in

x \ln (4) = \ln (26)

$x \ln (4) = \ln (26)$ by

\ln (4)

$\ln (4)$ .

\frac{x \ln (4)}{\ln (4)} = \frac{\ln (26)}{\ln (4)}

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (26)}{\ln (4)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

\ln (4)

$\ln (4)$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{x \ln (4)}{\ln (4)} = \frac{\ln (26)}{\ln (4)}

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (26)}{\ln (4)}$

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (26)}{\ln (4)}