Algebra Examples

e^{3 x} = 5

$e^{3 x} = 5$

Step 1

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

\ln (e^{3 x}) = \ln (5)

$\ln (e^{3 x}) = \ln (5)$

Step 2

Expand the left side.

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Step 2.1

Expand

\ln (e^{3 x})

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

3 x

$3 x$ outside the logarithm.

3 x \ln (e) = \ln (5)

$3 x \ln (e) = \ln (5)$

Step 2.2

The natural logarithm of

e

$e$ is

1

$1$ .

3 x \cdot 1 = \ln (5)

$3 x \cdot 1 = \ln (5)$

Step 2.3

Multiply

3

$3$ by

1

$1$ .

3 x = \ln (5)

$3 x = \ln (5)$

3 x = \ln (5)

$3 x = \ln (5)$

Step 3

Divide each term in

3 x = \ln (5)

$3 x = \ln (5)$ by

3

$3$ and simplify.

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Step 3.1

Divide each term in

3 x = \ln (5)

$3 x = \ln (5)$ by

3

$3$ .

\frac{3 x}{3} = \frac{\ln (5)}{3}

$\frac{3 x}{3} = \frac{\ln (5)}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

3

$3$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{3 x}{3} = \frac{\ln (5)}{3}

$\frac{3 x}{3} = \frac{\ln (5)}{3}$

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (5)}{3}

$x = \frac{\ln (5)}{3}$

x = \frac{\ln (5)}{3}

$x = \frac{\ln (5)}{3}$

x = \frac{\ln (5)}{3}

$x = \frac{\ln (5)}{3}$

x = \frac{\ln (5)}{3}

$x = \frac{\ln (5)}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \frac{\ln (5)}{3}

$x = \frac{\ln (5)}{3}$

Decimal Form:

x = 0.53647930 \dots

$x = 0.53647930 \dots$

e^{3 x} = 5

$e^{3 x} = 5$

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