# How do you solve #5e^(2x) = 500#?

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To solve (5e^{2x} = 500), first divide both sides by 5 to isolate the exponential term:

[ e^{2x} = \frac{500}{5} = 100 ]

Then, take the natural logarithm (ln) of both sides to eliminate the exponential:

[ \ln(e^{2x}) = \ln(100) ]

Using the property of logarithms that (\ln(e^y) = y):

[ 2x = \ln(100) ]

Finally, solve for (x) by dividing both sides by 2:

[ x = \frac{\ln(100)}{2} ]

Now, use the fact that (\ln(100) = 4.605) (approximately):

[ x = \frac{4.605}{2} ]

[ x = 2.3025 ]

Therefore, the solution to the equation (5e^{2x} = 500) is (x = 2.3025).

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