Precalculus Examples

$120 = 95 e^{- \frac{1}{30}} \cos (\frac{π}{4})$

Step 1

Simplify.

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Step 1.1

Divide each term in $120 = 95 e^{- \frac{1}{30}} \cos (\frac{π}{4})$ by $95$ .

$\frac{120}{95} = \frac{95 e^{- \frac{1}{30}} \cos (\frac{π}{4})}{95}$

Step 1.2

Cancel the common factor of $120$ and $95$ .

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Step 1.2.1

Factor $5$ out of $120$ .

$\frac{5 (24)}{95}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $5$ out of $95$ .

$\frac{5 \cdot 24}{5 \cdot 19}$

Step 1.2.2.2

Cancel the common factor.

$\frac{5 \cdot 24}{5 \cdot 19}$

Step 1.2.2.3

Rewrite the expression.

$\frac{24}{19}$

Step 1.3

Reduce by cancelling the common factors.

$\frac{24}{19} = e^{- \frac{1}{30}}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the left side $(\frac{24}{19})$ equals the exponent $(- \frac{1}{30})$ .

$\log_{e} (\frac{24}{19}) = - \frac{1}{30}$