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Popular >

simplify ln(1/(x^6))

Solution

simplify

ln (\frac{1}{x ^{6}})

Solution

- 6 ln (x)

Solution steps

ln (\frac{1}{x ^{6}})

Apply log rule:

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

ln (\frac{1}{x ^{6}}) = ln (1) - ln (x^{6})

= ln (1) - ln (x^{6})

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= ln (1) - 6 ln (x)

Apply log rule:

lo g_{a} (1) = 0

= 0 - 6 ln (x)

0 - 6 ln (x) = - 6 ln (x)

= - 6 ln (x)

Popular Examples

simplify log_{4}(3.188-1)+log_{4}(2(3.188)-5)simplify

lo g_{4} (3.188 - 1) + lo g_{4} (2 (3.188) - 5)

simplify-log_{10}(5.65*10^{-6})simplify

- lo g_{10} (5.65 \cdot 1 0^{- 6})

expand log_{10}((z^2)/4)expand

lo g_{10} (\frac{z ^{2}}{4})

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38 + 4 ln (86) - ln (9)

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ln (\frac{2 + 1}{2})

Frequently Asked Questions (FAQ)

What is ln(1/(x^6)) ?
The solution to ln(1/(x^6)) is -6ln(x)