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Popular >

simplify ln(1/(4^k))

Solution

simplify

ln (\frac{1}{4 ^{k}})

Solution

- 2 ln (2) k

Solution steps

ln (\frac{1}{4 ^{k}})

Apply log rule:

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

ln (\frac{1}{4 ^{k}}) = ln (1) - ln (4^{k})

= ln (1) - ln (4^{k})

Apply log rule:

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

ln (4^{k}) = k ln (4)

= ln (1) - k ln (4)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (4) k

0 - k ln (4) = - k ln (4)

= - ln (4) k

Simplify

ln (4) : 2 ln (2)

= - 2 ln (2) k

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Frequently Asked Questions (FAQ)

What is ln(1/(4^k)) ?
The solution to ln(1/(4^k)) is -2ln(2)k