SOLUTION: We are supposed to solve the equation 4^2x-1=32^x+2. So its supposed to be 4 to the 2x-1 power equals 32 to the x+2 power. I'm just having a hard time trying to figure this out.

Question 617384: We are supposed to solve the equation 4^2x-1=32^x+2.
So its supposed to be 4 to the 2x-1 power equals 32 to the x+2 power. I'm just having a hard time trying to figure this out. my mind does not think in logarithmic and exponential terms. Any help is greatly appreciated. Thank you for your time.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Notice how 4 and 32 are powers of 2. So rewrite them as such and simplify...

4^(2x-1) = 32^(x+2)

(2^2)^(2x-1) = (2^5)^(x+2)

2^(2(2x-1)) = 2^(5(x+2))

Since the bases are equal (to 2), the exponents must be equal. So....

2(2x-1) = 5(x+2)

4x-2 = 5x+10

4x-5x = 10+2

-x = 12

x = -12

So the solution is x = -12
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