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Popular >

simplify ln(1/(3^x))

Solution

simplify

ln (\frac{1}{3 ^{x}})

Solution

- ln (3) x

Solution steps

ln (\frac{1}{3 ^{x}})

Apply log rule:

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

ln (\frac{1}{3 ^{x}}) = ln (1) - ln (3^{x})

= ln (1) - ln (3^{x})

Apply log rule:

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

ln (3^{x}) = x ln (3)

= ln (1) - x ln (3)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (3) x

0 - x ln (3) = - x ln (3)

= - ln (3) x

Popular Examples

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simplify-log_{10}(6.8*10^{-6})simplify

- lo g_{10} (6.8 \cdot 1 0^{- 6})

d/(du)((t)(ln(t^2)+2ln(t)+2))

\frac{d}{d u} ((t) (ln (t^{2}) + 2 ln (t) + 2))

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Frequently Asked Questions (FAQ)

What is ln(1/(3^x)) ?
The solution to ln(1/(3^x)) is -ln(3)x