SOLUTION: solve 2^4x = 1/32 for x. equation orientation: https://gyazo.com/5d02dc1092b67927fadd216b0678dc7e

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Question 1205553: solve 2^4x = 1/32 for x.
equation orientation: https://gyazo.com/5d02dc1092b67927fadd216b0678dc7e
Found 3 solutions by Theo, ikleyn, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
equation is:
2^(4x) = 1/32

take the log of both sides of the equation to get:

log(2^(4x) = log(1/32)

by log rules, this becomes:
4x * log(2) = log(1/32)

solve for 4x to get:
4x = log(1/32) / log(2) = -5

replace 4x in the original equation to get:
2^(-5) = 1/32

2^(-5) is the same as 1/2^5 which is the same as 1/32.

you get 1/32 = 1/32, confirming the solution is correct.

Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website!
.

As the equation is presented in the link, it is = . It can be written in an equivalent form = . The exponential bases are equal; hence, the exponential indexes are the same 4x = -5. It implies x = . ANSWER. The solution is x = .

Solved.

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Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

The screenshot indicates the equation is

When you wrote 2^4x = 1/32, you have to be careful.
The 2^4x could mean either or
Since we want the second version, you should write it like 2^(4x)