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Popular >

expand ln(1/(25^k))

Solution

expand

ln (\frac{1}{2 5 ^{k}})

Solution

- 2 ln (5) k

Solution steps

ln (\frac{1}{2 5 ^{k}})

Apply log rule:

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

ln (\frac{1}{2 5 ^{k}}) = ln (1) - ln (2 5^{k})

= ln (1) - ln (2 5^{k})

Apply log rule:

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

ln (2 5^{k}) = k ln (25)

= ln (1) - k ln (25)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (25) k

0 - k ln (25) = - k ln (25)

= - ln (25) k

Simplify

ln (25) : 2 ln (5)

= - 2 ln (5) k

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Frequently Asked Questions (FAQ)

What is expand ln(1/(25^k)) ?
The solution to expand ln(1/(25^k)) is -2ln(5)k