Precalculus Examples

$\frac{- \log (\frac{6}{68})}{0.04}$

Step 1

Rewrite $\log (\frac{6}{68})$ as $\log (6) - \log (68)$ .

$\frac{- (\log (6) - \log (68))}{0.04}$

Step 2

Rewrite $\log (68)$ as $\log (2^{2} \cdot 17)$ .

$\frac{- (\log (6) - \log (2^{2} \cdot 17))}{0.04}$

Step 3

Rewrite $\log (2^{2} \cdot 17)$ as $\log (2^{2}) + \log (17)$ .

$\frac{- (\log (6) - (\log (2^{2}) + \log (17)))}{0.04}$

Step 4

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

$\frac{- (\log (6) - (2 \log (2) + \log (17)))}{0.04}$

Step 5

Apply the distributive property.

$\frac{- (\log (6) - (2 \log (2)) - \log (17))}{0.04}$

Step 6

Multiply $2$ by $- 1$ .

$\frac{- (\log (6) - 2 \log (2) - \log (17))}{0.04}$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite $\log (6)$ as $\log (2 (3))$ .

$\frac{- (\log (2 (3)) - 2 \log (2) - \log (17))}{0.04}$

Step 7.2

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$\frac{- (\log (2) + \log (3) - 2 \log (2) - \log (17))}{0.04}$

Step 7.3

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

$\frac{- (\log (3) - \log (2) - \log (17))}{0.04}$

Step 8

Move the negative in front of the fraction.

$- \frac{\log (3) - \log (2) - \log (17)}{0.04}$

Step 9

Log base $10$ of $3$ is approximately $0.47712125$ .

$- \frac{0.47712125 - \log (2) - \log (17)}{0.04}$

Step 10

Log base $10$ of $2$ is approximately $0.30102999$ .

$- \frac{0.47712125 - 1 \cdot 0.30102999 - \log (17)}{0.04}$

Step 11

Multiply $- 1$ by $0.30102999$ .

$- \frac{0.47712125 - 0.30102999 - \log (17)}{0.04}$

Step 12

Subtract $0.30102999$ from $0.47712125$ .

$- \frac{0.17609125 - \log (17)}{0.04}$

Step 13

Log base $10$ of $17$ is approximately $1.23044892$ .

$- \frac{0.17609125 - 1 \cdot 1.23044892}{0.04}$

Step 14

Multiply $- 1$ by $1.23044892$ .

$- \frac{0.17609125 - 1.23044892}{0.04}$

Step 15

Subtract $1.23044892$ from $0.17609125$ .

$- \frac{- 1.05435766}{0.04}$

Step 16

Divide $- 1.05435766$ by $0.04$ .

$- - 26.35894155$

Step 17

Multiply $- 1$ by $- 26.35894155$ .

$26.35894155$