Solve for x (logarithm)

2^x+2 = 8^x

I don't really understand how to do it...

take the log of both sides

log 2^x+2 = log 8^x

Bring exponents to the front

x+2 log 2 = x log 8

x+2 = x log 8 / log 2

x+2 / x = log 8 / log 2

Using calculator, log 8 / log 2 = 3

x+2 / x = 3

3x = x+2

2x = 2
x = 1

If the equation is 2^(x+2) = 8^x, then noting that 8 = 2^3 we get

2^(x+2) = (2^3)^x = 2^(3x). Now equate exponents to get

x + 2 = 3x ---> 2 = 2x ---> x = 1.

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