Precalculus Examples

$\frac{\log (\frac{19871.19}{19000})}{4 \cdot \log (1.0075)}$

Step 1

Rewrite $\log (\frac{19871.19}{19000})$ as $\log (19871.19) - \log (19000)$ .

$\frac{\log (19871.19) - \log (19000)}{4 \cdot \log (1.0075)}$

Step 2

Log base $10$ of $19871.19$ is approximately $4.29822387$ .

$\frac{4.29822387 - \log (19000)}{4 \cdot \log (1.0075)}$

Step 3

Rewrite $\log (19000)$ as $\log (2^{3} \cdot 5^{3} \cdot 19)$ .

$\frac{4.29822387 - \log (2^{3} \cdot 5^{3} \cdot 19)}{4 \cdot \log (1.0075)}$

Step 4

Rewrite $\log (2^{3} \cdot 5^{3} \cdot 19)$ as $\log (2^{3} \cdot 5^{3}) + \log (19)$ .

$\frac{4.29822387 - (\log (2^{3} \cdot 5^{3}) + \log (19))}{4 \cdot \log (1.0075)}$

Step 5

Raise $2$ to the power of $3$ .

$\frac{4.29822387 - (\log (8 \cdot 5^{3}) + \log (19))}{4 \cdot \log (1.0075)}$

Step 6

Raise $5$ to the power of $3$ .

$\frac{4.29822387 - (\log (8 \cdot 125) + \log (19))}{4 \cdot \log (1.0075)}$

Step 7

Multiply $8$ by $125$ .

$\frac{4.29822387 - (\log (1000) + \log (19))}{4 \cdot \log (1.0075)}$

Step 8

Logarithm base $10$ of $1000$ is $3$ .

$\frac{4.29822387 - (3 + \log (19))}{4 \cdot \log (1.0075)}$

Step 9

Apply the distributive property.

$\frac{4.29822387 - 1 \cdot 3 - \log (19)}{4 \cdot \log (1.0075)}$

Step 10

Multiply $- 1$ by $3$ .

$\frac{4.29822387 - 3 - \log (19)}{4 \cdot \log (1.0075)}$

Step 11

Subtract $3$ from $4.29822387$ .

$\frac{1.29822387 - \log (19)}{4 \cdot \log (1.0075)}$

Step 12

Subtract $\log (19)$ from $1.29822387$ .

$\frac{0.01947027}{4 \cdot \log (1.0075)}$

Step 13

Log base $10$ of $1.0075$ is approximately $0.00324505$ .

$\frac{0.01947027}{4 \cdot 0.00324505}$

Step 14

Multiply $4$ by $0.00324505$ .

$\frac{0.01947027}{0.01298021}$

Step 15

Divide $0.01947027$ by $0.01298021$ .

$1.49999584$