Algebra Examples

3^{x} = 4

$3^{x} = 4$

Step 1

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

\ln (3^{x}) = \ln (4)

$\ln (3^{x}) = \ln (4)$

Step 2

Expand

\ln (3^{x})

$\ln (3^{x})$ by moving

x

$x$ outside the logarithm.

x \ln (3) = \ln (4)

$x \ln (3) = \ln (4)$

Step 3

Divide each term in

x \ln (3) = \ln (4)

$x \ln (3) = \ln (4)$ by

\ln (3)

$\ln (3)$ and simplify.

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Step 3.1

Divide each term in

x \ln (3) = \ln (4)

$x \ln (3) = \ln (4)$ by

\ln (3)

$\ln (3)$ .

\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4)}{\ln (3)}

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4)}{\ln (3)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

\ln (3)

$\ln (3)$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4)}{\ln (3)}

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (4)}{\ln (3)}$

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (4)}{\ln (3)}

$x = \frac{\ln (4)}{\ln (3)}$

x = \frac{\ln (4)}{\ln (3)}

$x = \frac{\ln (4)}{\ln (3)}$

x = \frac{\ln (4)}{\ln (3)}

$x = \frac{\ln (4)}{\ln (3)}$

x = \frac{\ln (4)}{\ln (3)}

$x = \frac{\ln (4)}{\ln (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \frac{\ln (4)}{\ln (3)}

$x = \frac{\ln (4)}{\ln (3)}$

Decimal Form:

x = 1.26185950 \dots

$x = 1.26185950 \dots$

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