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

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

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simplify ln(1/(121^k))

simplify

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

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 6 lo g_{10} (z)

- lo g_{10} (1.75 \cdot 1 0^{- 5})

lo g_{2} (\frac{4 x + 1}{x})

2 lo g_{4} (x) - lo g_{4} (y) - \frac{1}{2} lo g_{4} (z)

lo g_{5} (\frac{3 x + 2}{x + 1})