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Popular >

simplify ln(1/(9^k))

Solution

simplify

ln (\frac{1}{9 ^{k}})

Solution

- 2 ln (3) k

Solution steps

ln (\frac{1}{9 ^{k}})

Apply log rule:

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

ln (\frac{1}{9 ^{k}}) = ln (1) - ln (9^{k})

= ln (1) - ln (9^{k})

Apply log rule:

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

ln (9^{k}) = k ln (9)

= ln (1) - k ln (9)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (9) k

0 - k ln (9) = - k ln (9)

= - ln (9) k

Simplify

ln (9) : 2 ln (3)

= - 2 ln (3) k

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Frequently Asked Questions (FAQ)

What is ln(1/(9^k)) ?
The solution to ln(1/(9^k)) is -2ln(3)k