Precalculus Examples

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

Step 1

Multiply $10^{12}$ by $10^{8}$ by adding the exponents.

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Step 1.1

Move $10^{8}$ .

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

Step 1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.3

Add $8$ and $12$ .

$10 \log (10^{20} \cdot 4.8)$

Step 2

Raise $10$ to the power of $20$ .

$10 \log (100000000000000000000 \cdot 4.8)$

Step 3

Multiply $100000000000000000000$ by $4.8$ .

$10 \log (480000000000000000000)$

Step 4

Log base $10$ of $480000000000000000000$ is approximately $20.68124123$ .

$10 \cdot 20.68124123$

Step 5

Multiply $10$ by $20.68124123$ .

$206.81241237$