How do you expand $ln((2^-2)(3^1))/ln((2)(3))^-4$ ?

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Answer 1 · 2016-09-13T11:20:08

We have: $(ln((2^(- 2)) (3^(1)))) / (ln((2) (3))^(- 4))$

$= (ln(((1) / (4)) (3))) / (ln(((2) (3))^(- 4)))$

$= (ln((3) / (4))) / (ln(6^(- 4))$

Using the laws of logarithms:

$= (ln((3) / (4))) / (- 4 ln(6))$

$= - (ln((3) / (4))) / (4 ln(6))$

How do you expand ln((2^-2)(3^1))/ln((2)(3))^-4ln((2^-2)(3^1))/ln((2)(3))^-4?