Precalculus Examples

$10 \log (\frac{115}{10^{- 12}})$

Step 1

Move $10^{- 12}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$10 \log (115 \cdot 10^{12})$

Step 2

Move the decimal point in $115$ to the left by $2$ places and increase the power of $10^{12}$ by $2$ .

$10 \log (1.15 \cdot 10^{14})$

Step 3

Simplify $10 \log (1.15 \cdot 10^{14})$ by moving $10$ inside the logarithm.

$\log ({(1.15 \cdot 10^{14})}^{10})$

Step 4

Apply the product rule to $1.15 \cdot 10^{14}$ .

$\log ({1.15}^{10} \cdot {(10^{14})}^{10})$

Step 5

Raise $1.15$ to the power of $10$ .

$\log (4.04555773 \cdot {(10^{14})}^{10})$

Step 6

Multiply the exponents in ${(10^{14})}^{10}$ .

Tap for more steps...

Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (4.04555773 \cdot 10^{14 \cdot 10})$

Step 6.2

Multiply $14$ by $10$ .

$\log (4.04555773 \cdot 10^{140})$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$\log (4.04555773 \cdot 10^{140})$

Expanded Form:

$140.6069784$