Precalculus Examples

$2 \log (5) - \frac{1}{2} \cdot \log (7) - \log (3.8)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (5)$ by moving $2$ inside the logarithm.

$\log (5^{2}) - \frac{1}{2} \cdot \log (7) - \log (3.8)$

Step 1.2

Raise $5$ to the power of $2$ .

$\log (25) - \frac{1}{2} \cdot \log (7) - \log (3.8)$

Step 1.3

Multiply $- \frac{1}{2} \log (7)$ .

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Step 1.3.1

Reorder $\log (7)$ and $\frac{1}{2}$ .

$\log (25) - (\frac{1}{2} \log (7)) - \log (3.8)$

Step 1.3.2

Simplify $\frac{1}{2} \log (7)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log (25) - \log (7^{\frac{1}{2}}) - \log (3.8)$

Step 1.4

Log base $10$ of $3.8$ is approximately $0.57978359$ .

$\log (25) - \log (7^{\frac{1}{2}}) - 1 \cdot 0.57978359$

Step 1.5

Multiply $- 1$ by $0.57978359$ .

$\log (25) - \log (7^{\frac{1}{2}}) - 0.57978359$

Step 2

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

$\log (\frac{25}{7^{\frac{1}{2}}}) - 0.57978359$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{25}{7^{\frac{1}{2}}}) - 0.57978359$

Decimal Form:

$0.39560739 \dots$