How do you simplify a log with an exponent in the base? Suppose you had: \log_{x^b}(y)

Natasha Gill

Natasha Gill

Answered question

2022-01-21

How do you simplify a log with an exponent in the base?
Suppose you had:
logxb(y)
How can you simplify this? Do you use the change of base formula?
Note: I tried to come up with something similar to a homework problem without actually being a homework problem. I think this is the most simple form.

Answer & Explanation

trasahed

trasahed

Beginner2022-01-22Added 14 answers

We have your original function
logxb(y)=z
Following basic rules for logarithms, assuming x,y,z>0
(xb)z=y
xbz=y
logx(y)=bz
Thus z can be expressed as
z=logx(y)b
Armani Dyer

Armani Dyer

Beginner2022-01-23Added 10 answers

You can calculate
ln(y)ln(xb)=ln(y)bln(x)=logx(y)b

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