Precalculus Examples

$10 \cdot \log (\frac{4.3 \cdot 10^{- 6}}{10^{- 12}})$

Step 1

Divide using scientific notation.

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Step 1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$10 \cdot \log ((\frac{4.3}{1}) (\frac{10^{- 6}}{10^{- 12}}))$

Step 1.2

Divide $4.3$ by $1$ .

$10 \cdot \log (4.3 \frac{10^{- 6}}{10^{- 12}})$

Step 1.3

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$10 \cdot \log (4.3 \cdot 10^{- 6 - 12 \cdot - 1})$

Step 1.4

Multiply $- 12$ by $- 1$ .

$10 \cdot \log (4.3 \cdot 10^{- 6 + 12})$

Step 1.5

Add $- 6$ and $12$ .

$10 \cdot \log (4.3 \cdot 10^{6})$

Step 2

Simplify $10 \log (4.3 \cdot 10^{6})$ by moving $10$ inside the logarithm.

$\log ({(4.3 \cdot 10^{6})}^{10})$

Step 3

Apply the product rule to $4.3 \cdot 10^{6}$ .

$\log ({4.3}^{10} \cdot {(10^{6})}^{10})$

Step 4

Raise $4.3$ to the power of $10$ .

$\log (2161148.23132842 \cdot {(10^{6})}^{10})$

Step 5

Multiply the exponents in ${(10^{6})}^{10}$ .

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Step 5.1

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

$\log (2161148.23132842 \cdot 10^{6 \cdot 10})$

Step 5.2

Multiply $6$ by $10$ .

$\log (2161148.23132842 \cdot 10^{60})$

Step 6

Move the decimal point in $2161148.23132842$ to the left by $6$ places and increase the power of $10^{60}$ by $6$ .

$\log (2.16114823 \cdot 10^{66})$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$\log (2.16114823 \cdot 10^{66})$

Expanded Form:

$66.33468455$