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

Question 385067: Solve: 4^(2x+1)=8^(x+4)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

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:

When raising a power to a power, the rule for the exponents is to multiply them. So the equation simplifies as follows:

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
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