Precalculus Examples

$\log (90) - 0.2 \log (12 + 1)$

Step 1

Add $12$ and $1$ .

$\log (90) - 0.2 \log (13)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log (90)$ as $\log (2 \cdot 3^{2} \cdot 5)$ .

$\log (2 \cdot 3^{2} \cdot 5) - 0.2 \log (13)$

Step 2.2

Rewrite $\log (2 \cdot 3^{2} \cdot 5)$ as $\log (2 \cdot 3^{2}) + \log (5)$ .

$\log (2 \cdot 3^{2}) + \log (5) - 0.2 \log (13)$

Step 2.3

Simplify each term.

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Step 2.3.1

Rewrite $\log (2 \cdot 3^{2})$ as $\log (2) + \log (3^{2})$ .

$\log (2) + \log (3^{2}) + \log (5) - 0.2 \log (13)$

Step 2.3.2

Expand $\log (3^{2})$ by moving $2$ outside the logarithm.

$\log (2) + 2 \log (3) + \log (5) - 0.2 \log (13)$

Step 2.4

Multiply $- 0.2$ by $\log (13)$ .

$\log (2) + 2 \log (3) + \log (5) - 0.22278867$

Step 3

Subtract $0.22278867$ from $\log (2)$ .

$2 \log (3) + \log (5) + 0.07824132$

Step 4

Add $2 \log (3)$ and $0.07824132$ .

$1.03248383 + \log (5)$

Step 5

Add $1.03248383$ and $\log (5)$ .

$1.73145383$