Algebra Examples

$87 e^{0.3 x} = 5918$

Step 1

Divide each term in $87 e^{0.3 x} = 5918$ by $87$ and simplify.

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Step 1.1

Divide each term in $87 e^{0.3 x} = 5918$ by $87$ .

$\frac{87 e^{0.3 x}}{87} = \frac{5918}{87}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $87$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{87 e^{0.3 x}}{87} = \frac{5918}{87}$

Step 1.2.1.2

Divide $e^{0.3 x}$ by $1$ .

$e^{0.3 x} = \frac{5918}{87}$

Step 2

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

$\ln (e^{0.3 x}) = \ln (\frac{5918}{87})$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{0.3 x})$ by moving $0.3 x$ outside the logarithm.

$0.3 x \ln (e) = \ln (\frac{5918}{87})$

Step 3.2

The natural logarithm of $e$ is $1$ .

$0.3 x \cdot 1 = \ln (\frac{5918}{87})$

Step 3.3

Multiply $0.3$ by $1$ .

$0.3 x = \ln (\frac{5918}{87})$

Step 4

Divide each term in $0.3 x = \ln (\frac{5918}{87})$ by $0.3$ and simplify.

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Step 4.1

Divide each term in $0.3 x = \ln (\frac{5918}{87})$ by $0.3$ .

$\frac{0.3 x}{0.3} = \frac{\ln (\frac{5918}{87})}{0.3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.3 x}{0.3} = \frac{\ln (\frac{5918}{87})}{0.3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{5918}{87})}{0.3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Replace $e$ with an approximation.

$x = \frac{\log_{2.71828182} (\frac{5918}{87})}{0.3}$

Step 4.3.2

Divide $5918$ by $87$ .

$x = \frac{\log_{2.71828182} (68.0229885)}{0.3}$

Step 4.3.3

Log base $2.71828182$ of $68.0229885$ is approximately $4.21984571$ .

$x = \frac{4.21984571}{0.3}$

Step 4.3.4

Divide $4.21984571$ by $0.3$ .

$x = 14.06615238$