Question about basic exponential/logarithm properties Solve for k: e <mrow class="MJX-

Gretchen Schwartz

Gretchen Schwartz

Answered question

2022-07-01

Question about basic exponential/logarithm properties
Solve for k:
e k / 2 = a
Solution:
e 2 k = a
k / 2 = l n a
k = 2 l n a
= l n a 2
My question is: why does 2 l n a = l n a 2 ? Why can you transfer the 2 to be an exponent of a?

Answer & Explanation

Salma Bradley

Salma Bradley

Beginner2022-07-02Added 13 answers

Because logarithms map multiplication to addition:
ln a b = ln a + ln b
So in particular:
ln a 2 = ln a + ln a = 2 ln a

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