Algebra Examples

3^{x} = 10

$3^{x} = 10$

Step 1

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

ln (3^{x}) = ln (10)

$\ln (3^{x}) = \ln (10)$

Step 2

Expand

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

$x$ outside the logarithm.

$x \ln (3) = \ln (10)$

Step 3

Divide each term in

$x \ln (3) = \ln (10)$ by

$\ln (3)$ and simplify.

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Step 3.1

Divide each term in

$x \ln (3) = \ln (10)$ by

$\ln (3)$ .

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (10)}{\ln (3)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$\ln (3)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (10)}{\ln (3)}$

Step 3.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{\ln (10)}{\ln (3)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (10)}{\ln (3)}$

Decimal Form:

$x = 2.09590327 \dots$

$3^{x} = 10$

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