Precalculus Examples

$\log (20 {(1.4)}^{x})$

Rewrite $\log (20 {(1.4)}^{x})$ as $\log (20) + \log ({(1.4)}^{x})$ .

$\log (20) + \log ({(1.4)}^{x})$

Expand $\log ({(1.4)}^{x})$ by moving $x$ outside the logarithm.

$\log (20) + x \log (1.4)$

Log base $10$ of $1.4$ is approximately $0.14612803$ .

$\log (20) + x \cdot 0.14612803$

Simplify each term.

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Rewrite $\log (20)$ as $\log (2^{2} \cdot 5)$ .

$\log (2^{2} \cdot 5) + x \cdot 0.14612803$

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

$\log (2^{2}) + \log (5) + x \cdot 0.14612803$

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

$2 \log (2) + \log (5) + x \cdot 0.14612803$

Move $0.14612803$ to the left of $x$ .

$2 \log (2) + \log (5) + 0.14612803 x$