Finite Math Examples

$\log (e^{x}) = 13.6$

Step 1

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

$x \log (e)$

Step 2

The expanded equation is $x \log (e) = 13.6$ .

$x \log (e) = 13.6$

Step 3

Divide each term in $x \log (e) = 13.6$ by $\log (e)$ and simplify.

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Step 3.1

Divide each term in $x \log (e) = 13.6$ by $\log (e)$ .

$\frac{x \log (e)}{\log (e)} = \frac{13.6}{\log (e)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\log (e)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \log (e)}{\log (e)} = \frac{13.6}{\log (e)}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{13.6}{\log (e)}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Replace $e$ with an approximation.

$x = \frac{13.6}{\log (2.71828182)}$

Step 3.3.2

Log base $10$ of $2.71828182$ is approximately $0.43429448$ .

$x = \frac{13.6}{0.43429448}$

Step 3.3.3

Divide $13.6$ by $0.43429448$ .

$x = 31.31515726$