What is ln((4.6*10^{-5})/(0.0049)) ?

The solution to ln((4.6*10^{-5})/(0.0049)) is ln(4.6)-5ln(10)-ln(0.0049)

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simplify ln((4.6*10^{-5})/(0.0049))

simplify

ln (\frac{4.6 \cdot 1 0 ^{- 5}}{0.0049})

ln (4.6) - 5 ln (10) - ln (0.0049)

Decimal Notation

- 4.66834 \dots

Solution steps

ln (\frac{4.6 \cdot 1 0 ^{- 5}}{0.0049})

Apply log rule:

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

ln (\frac{4.6 \cdot 1 0 ^{- 5}}{0.0049}) = ln (4.6 \cdot 1 0^{- 5}) - ln (0.0049)

= ln (1 0^{- 5} \cdot 4.6) - ln (0.0049)

Apply log rule:

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

ln (4.6 \cdot 1 0^{- 5}) = ln (4.6) + ln (1 0^{- 5})

= ln (4.6) + ln (1 0^{- 5}) - ln (0.0049)

Apply log rule:

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

ln (1 0^{- 5}) = - 5 ln (10)

= ln (4.6) - 5 ln (10) - ln (0.0049)

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What is ln((4.6*10^{-5})/(0.0049)) ?
The solution to ln((4.6*10^{-5})/(0.0049)) is ln(4.6)-5ln(10)-ln(0.0049)