Precalculus Examples

$10 \log (10^{12} \cdot 4.8 \cdot 10^{8})$

Step 1

Rewrite $\log (10^{12} \cdot 4.8 \cdot 10^{8})$ as $\log (10^{12}) + \log (4.8 \cdot 10^{8})$ .

$10 (\log (10^{12}) + \log (4.8 \cdot 10^{8}))$

Step 2

Rewrite $\log (4.8 \cdot 10^{8})$ as $\log (4.8) + \log (10^{8})$ .

$10 (\log (10^{12}) + \log (4.8) + \log (10^{8}))$

Step 3

Expand $\log (10^{12})$ by moving $12$ outside the logarithm.

$10 (12 \log (10) + \log (4.8) + \log (10^{8}))$

Step 4

Expand $\log (10^{8})$ by moving $8$ outside the logarithm.

$10 (12 \log (10) + \log (4.8) + 8 \log (10))$

Step 5

Logarithm base $10$ of $10$ is $1$ .

$10 (12 \cdot 1 + \log (4.8) + 8 \log (10))$

Step 6

Log base $10$ of $4.8$ is approximately $0.68124123$ .

$10 (12 \cdot 1 + 0.68124123 + 8 \log (10))$

Step 7

Logarithm base $10$ of $10$ is $1$ .

$10 (12 \cdot 1 + 0.68124123 + 8 \cdot 1)$

Step 8

Multiply $12$ by $1$ .

$10 (12 + 0.68124123 + 8 \cdot 1)$

Step 9

Multiply $8$ by $1$ .

$10 (12 + 0.68124123 + 8)$

Step 10

Add $0.68124123$ and $8$ .

$10 (12 + 8.68124123)$

Step 11

Add $12$ and $8.68124123$ .

$10 \cdot 20.68124123$

Step 12

Multiply $10$ by $20.68124123$ .

$206.81241237$