What is expand ln(1/(121^k)) ?

The solution to expand ln(1/(121^k)) is -2ln(11)k

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expand ln(1/(121^k))

expand

ln (\frac{1}{12 1 ^{k}})

- 2 ln (11) k

Solution steps

ln (\frac{1}{12 1 ^{k}})

Apply log rule:

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

ln (\frac{1}{12 1 ^{k}}) = ln (1) - ln (12 1^{k})

= ln (1) - ln (12 1^{k})

Apply log rule:

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

ln (12 1^{k}) = k ln (121)

= ln (1) - k ln (121)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (121) k

0 - k ln (121) = - k ln (121)

= - ln (121) k

Simplify

ln (121) : 2 ln (11)

= - 2 ln (11) k

\frac{1}{3} lo g_{10} (x^{3} + 1) + \frac{1}{2} lo g_{10} (x^{2} + 1)

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

lo g_{4} (x^{2} - 64) - 4 lo g_{4} (x + 8)

ln (\frac{z}{x y})

lo g_{3} (\frac{100}{27 x})

What is expand ln(1/(121^k)) ?
The solution to expand ln(1/(121^k)) is -2ln(11)k