Precalculus Examples

$2 = 2800 {(1 + \frac{7}{12})}^{12 (9.9)}$

Step 1

Simplify.

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Step 1.1

Multiply $12$ by $9.9$ .

$2 = 2800 {(1 + \frac{7}{12})}^{118.8}$

Step 1.2

Divide each term in $2 = 2800 {(1 + \frac{7}{12})}^{118.8}$ by $2800$ .

$\frac{2}{2800} = \frac{2800 {(1 + \frac{7}{12})}^{118.8}}{2800}$

Step 1.3

Cancel the common factor of $2$ and $2800$ .

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Step 1.3.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{2800}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $2800$ .

$\frac{2 \cdot 1}{2 \cdot 1400}$

Step 1.3.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 1400}$

Step 1.3.2.3

Rewrite the expression.

$\frac{1}{1400}$

Step 1.4

Reduce by cancelling the common factors.

$\frac{1}{1400} = {(1 + \frac{7}{12})}^{118.8}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(1 + \frac{7}{12})$ of the left side $(\frac{1}{1400})$ equals the exponent $(118.8)$ .

$\log_{1 + \frac{7}{12}} (\frac{1}{1400}) = 118.8$