Math CentralQuandaries & Queries


Question from Dave, a student:

4^x = 2^x + 12 solve for x.

It's obvious the answer is 2, but using logs I get the answer 3.58 after going via:

log(4)x = log(2)x +log(12)

Please tell me where I am going wrong.

Hi Dave,

You took the log of both sides to get

log(4x) = log(2x + 12)

but log(2x + 12) is not equal to log(2x) + log(12). What is true is that log(2x × 12) = log(2x) + log(12) but that's no help here.

I think your first solution is best "It's obvious the answer is 2" but another method is to use the fact that 4 = 22 and use the laws of exponents to see that 4x = (22)x = 22x = (2x)2. Thus

4x = 2x + 12
(2x)2 = 2x + 12
(2x)2 - 2x - 12 = 0

Can you complete the solutiion?

If you need more help write back,

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