What is (ln(0.24)-ln(0.12))/(0.12)*12 ?

The solution to (ln(0.24)-ln(0.12))/(0.12)*12 is (12ln(2))/(0.12)

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simplify (ln(0.24)-ln(0.12))/(0.12)*12

simplify

\frac{ln ( 0.24 ) - ln ( 0.12 )}{0.12} \cdot 12

\frac{12 ln ( 2 )}{0.12}

Decimal Notation

69.31471 \dots

Solution steps

\frac{ln ( 0.24 ) - ln ( 0.12 )}{0.12} \cdot 12

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (0.24) - ln (0.12) = ln (\frac{0.24}{0.12})

= 12 \cdot \frac{ln ( \frac{0.24}{0.12} )}{0.12}

Divide the numbers:

\frac{0.24}{0.12} = 2

= \frac{ln ( 2 )}{0.12} \cdot 12

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{ln ( 2 ) \cdot 12}{0.12}

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What is (ln(0.24)-ln(0.12))/(0.12)*12 ?
The solution to (ln(0.24)-ln(0.12))/(0.12)*12 is (12ln(2))/(0.12)