Finite Math Examples

$x = \frac{\log_{5} (10000) - \log_{5} (1000)}{4 \log_{5} (1.0125)}$

Step 1

Simplify the numerator.

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Step 1.1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$x = \frac{\log_{5} (\frac{10000}{1000})}{4 \log_{5} (1.0125)}$

Step 1.2

Divide $10000$ by $1000$ .

$x = \frac{\log_{5} (10)}{4 \log_{5} (1.0125)}$

Step 2

Simplify $4 \log_{5} (1.0125)$ by moving $4$ inside the logarithm.

$x = \frac{\log_{5} (10)}{\log_{5} ({1.0125}^{4})}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $1.0125$ to the power of $4$ .

$x = \frac{\log_{5} (10)}{\log_{5} (1.05094533)}$

Step 3.2

Log base $5$ of $1.05094533$ is approximately $0.03087418$ .

$x = \frac{\log_{5} (10)}{0.03087418}$

Step 4

Log base $5$ of $10$ is approximately $1.43067655$ .

$x = \frac{1.43067655}{0.03087418}$

Step 5

Divide $1.43067655$ by $0.03087418$ .

$x = 46.33892908$