SOLUTION: Solve: 4^(2x+1)=8^(x+4)

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Question 385067: Solve: 4^(2x+1)=8^(x+4)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%282x%2B1%29=8%5E%28x%2B4%29
With variables in exponents we would usually use logarithms to solve an equation like this. And we could do so on this equation. However, since 4 and 8 are both powers of 2 we can express both sides of the equation as powers of 2. Such an equation is easier to solve this way than with logarithms:
%282%5E2%29%5E%282x%2B1%29+=+%282%5E3%29%5E%28x%2B4%29
When raising a power to a power, the rule for the exponents is to multiply them. So the equation simplifies as follows:
2%5E%282%2A%282x%2B1%29%29+=+2%5E%283%2A%28x%2B4%29%29
2%5E%284x%2B2%29+=+2%5E%283x%2B12%29
Now the equation says that two powers of 2 are equal. The only way this can be true is if the exponents are equal, too. So:
4x + 2 = 3x + 12
This is easy to solve. Subtract 3x from each side:
x + 2 = 12
Subtract 2 from each side:
x = 10