Equation Challenge: Solve an Exponential Equation with Square Roots

This video explains how to solve an exponential equation.

[joemama-ksty]

I did it without needing to know power rules.

1.i can rewrite the equation to b Sqrt(6)^a = 36 which is 4 since sqrt(6)^2 makes 6 so sqrt(6)^4 must be 6*6 =36.

2. Since i know a =4 =sqrt(12+(sqrt(x)) i can rewrite it as 4=sqrt(b) which is b=16

3. Now b = 16 = 12+sqrt(x), which is easy to solve since it becomes 4 = sqrt(x) which i just solved in step 2 which was 16. Therefore, x = 16

Math rocks cause you can find multiple paths for the same amswer

[radyenikanal]

Some of people say this is wrong but this is true

[specialagentdalecooper]

Well that's a lot more elegant than my solution which was to take the log of both sides to remove the exponent, lol. Messy but I got the same result in the end.

Full solution:

sqrt(12+sqrt(x)) * log(sqrt(6)) = log36
sqrt(12+sqrt(x))= log36/log(sqrt(6))
sqrt(12+sqrt(x))=4
12+sqrt(x) = 16
sqrt(x)=4
x=16

[jensraab]

I did everything the same except for the first step.
I simply rewrote 36 as (√6)⁴ and therefore skipped several of your steps directly to √(12+√x) = 4.
In the end it doesn't matter, of course.