What is ln(2.4e^{-7})-14 ?

The solution to ln(2.4e^{-7})-14 is ln(2.4)-21

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simplify ln(2.4e^{-7})-14

simplify

ln (2.4 e^{- 7}) - 14

ln (2.4) - 21

Decimal Notation

- 20.12453 \dots

Solution steps

ln (2.4 e^{- 7}) - 14

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2.4 e^{- 7}) = ln (2.4) + ln (e^{- 7})

= ln (2.4) + ln (e^{- 7}) - 14

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{- 7}) = - 7 ln (e)

= ln (2.4) - 7 ln (e) - 14

7 ln (e) = 7

= ln (2.4) - 7 - 14

Subtract the numbers:

- 7 - 14 = - 21

= ln (2.4) - 21

\frac{1}{15} ln (\frac{0.267 - 0.017}{0.095 - 0.017})

0.56 + 0.027 \cdot ln (\frac{1 0 ^{16}}{1.5 \cdot 1 0 ^{10}})

- \frac{4}{13} lo g_{2} (\frac{4}{13}) - \frac{9}{13} lo g_{2} (\frac{9}{13})

lo g_{10} (\frac{x}{z ^{5} y})

lo g_{3} (\frac{1}{( x ^{2} y 3 ^{z} )})