Solve the equation: 2^(2x+1)=(1/32)^x

reevelingw97

reevelingw97

Answered question

2022-11-10

Solve the equation: 2 2 x + 1 = ( 1 32 ) x
Having trouble with this problem:
2 2 x + 1 = 1 32 x
Do I need to set the exponents equal to each other?

Answer & Explanation

Geovanni Shelton

Geovanni Shelton

Beginner2022-11-11Added 15 answers

You you can equate exponents only if you have the same base.
2 2 x + 1 = 2 x log 2 1 32
so then we have
2 x + 1 = x log 2 1 32 = x log 2 2 5 = 5 x
and
2 x + 1 = 5 x
so
x = 1 7
You could have also taken the log 2 of both sides and it would have given you the same answer.

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