Determine if the equation is valid/true The equation is:

amonitas3zeb

amonitas3zeb

Answered question

2022-03-25

Determine if the equation is valid/true
The equation is:
logb3+232=2logb(3+2).
I can get as far as:
logb(3+2)logb(32)=2logb(3+2)
Which looks almost too simple, but I can't get the signs to match up right to solve the problem. Do I need to further break out the logarithmic functions that are there?

Answer & Explanation

Esteban Sloan

Esteban Sloan

Beginner2022-03-26Added 21 answers

logb(3+2)logb(32)=2logb(3+2)
is equivalent to
logb(3+2)=logb(32)+2logb(3+2)
which is equivalent to
logb(3+2)=logb((32)(3+2)2)
which you can multiply out to check, or you might spot
(32)(3+2)=3222=1
Jamie Maldonado

Jamie Maldonado

Beginner2022-03-27Added 10 answers

HINT 1 (ab)(a+b)=a2b2 for any numbers a and b.
HINT 2. Note that
3+232=(3+232)(3+23+2)=(3+2)232.

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