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

Answer 1

Sadie Ackerman

#x=ln(100)/2#

We can start off by dividing both sides by #5#. We get

#e^(2x)=100#

We can take the natural log of both sides to cancel out base #e#. We get

#ln(e^(2x))=ln(100)#

#=>2x=ln(100)#

#x=ln(100)/2#

I chose to not evaluate #ln(100)# so we could get an exact answer, but it will evaluate to about #4.6#, and dividing it by #2# would give us about #2.3#.

Hope this helps!

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Answer 2

Serenity Johnson

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.