Precalculus Examples

$\frac{1}{1.54 \cdot 10^{- 8}} \cdot \ln (\frac{0.0681 + 0.0391}{0.0681})$

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.

$(\frac{1}{1.54}) (\frac{1}{10^{- 8}}) \cdot \ln (\frac{0.0681 + 0.0391}{0.0681})$

Step 1.2

Divide $1$ by $1.54$ .

$0.\overline{649350} \frac{1}{10^{- 8}} \cdot \ln (\frac{0.0681 + 0.0391}{0.0681})$

Step 1.3

Move $10^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$0.\overline{649350} \cdot 10^{8} \cdot \ln (\frac{0.0681 + 0.0391}{0.0681})$

Step 2

Move the decimal point in $0.\overline{649350}$ to the right by $1$ place and decrease the power of $10^{8}$ by $1$ .

$6.\overline{493506} \cdot 10^{7} \cdot \ln (\frac{0.0681 + 0.0391}{0.0681})$

Step 3

Add $0.0681$ and $0.0391$ .

$6.\overline{493506} \cdot 10^{7} \cdot \ln (\frac{0.1072}{0.0681})$

Step 4

Divide $0.1072$ by $0.0681$ .

$6.\overline{493506} \cdot 10^{7} \cdot \ln (1.57415565)$

Step 5

Simplify $6.\overline{493506} \ln (1.57415565)$ by moving $6.\overline{493506}$ inside the logarithm.

$10^{7} \ln ({1.57415565}^{6.\overline{493506}})$

Step 6

Raise $10$ to the power of $7$ .

$10000000 \ln ({1.57415565}^{6.\overline{493506}})$

Step 7

Raise $1.57415565$ to the power of $6.\overline{493506}$ .

$10000000 \ln (19.03401236)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$10000000 \ln (19.03401236)$

Decimal Form:

$29462275.031249$