Precalculus Examples

$\frac{\log (\frac{1000}{600})}{4 \log (1 + \frac{0.07}{4})}$

Step 1

Cancel the common factor of $1000$ and $600$ .

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Step 1.1

Factor $200$ out of $1000$ .

$\frac{\log (\frac{200 (5)}{600})}{4 \log (1 + \frac{0.07}{4})}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $200$ out of $600$ .

$\frac{\log (\frac{200 \cdot 5}{200 \cdot 3})}{4 \log (1 + \frac{0.07}{4})}$

Step 1.2.2

Cancel the common factor.

$\frac{\log (\frac{200 \cdot 5}{200 \cdot 3})}{4 \log (1 + \frac{0.07}{4})}$

Step 1.2.3

Rewrite the expression.

$\frac{\log (\frac{5}{3})}{4 \log (1 + \frac{0.07}{4})}$

Step 2

Simplify $4 \log (1 + \frac{0.07}{4})$ by moving $4$ inside the logarithm.

$\frac{\log (\frac{5}{3})}{\log ({(1 + \frac{0.07}{4})}^{4})}$

Step 3

Simplify the denominator.

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Step 3.1

Divide $0.07$ by $4$ .

$\frac{\log (\frac{5}{3})}{\log ({(1 + 0.0175)}^{4})}$

Step 3.2

Add $1$ and $0.0175$ .

$\frac{\log (\frac{5}{3})}{\log ({1.0175}^{4})}$

Step 3.3

Raise $1.0175$ to the power of $4$ .

$\frac{\log (\frac{5}{3})}{\log (1.07185903)}$

Step 3.4

Log base $10$ of $1.07185903$ is approximately $0.03013767$ .

$\frac{\log (\frac{5}{3})}{0.03013767}$

Step 4

Divide $5$ by $3$ .

$\frac{\log (1.\overline{6})}{0.03013767}$

Step 5

Log base $10$ of $1.\overline{6}$ is approximately $0.22184874$ .

$\frac{0.22184874}{0.03013767}$

Step 6

Divide $0.22184874$ by $0.03013767$ .

$7.36117748$