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How do you solve #14e^(3x+2)=560#?

Answer 1

Sophie Adams

#x= (ln40-2)/3#

If #color(white)("XXX")14e^(3x+2) = 560# then (after dividing both sides by #14#) #color(white)("XXX")e^(3x+2) = 40#

By taking the natural logarithm of both sides: #color(white)("XXX")3x+2 = ln40#

#color(white)("XXX")3x = ln40-2#

#color(white)("XXX")x = (ln(40)-2)/3#

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Answer 2

Sadie Ackerman

To solve (14e^{3x+2} = 560), first divide both sides by 14 to isolate the exponential term:

[ e^{3x+2} = \frac{560}{14} ]

[ e^{3x+2} = 40 ]

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

[ \ln(e^{3x+2}) = \ln(40) ]

[ 3x + 2 = \ln(40) ]

Now, isolate (x) by subtracting 2 from both sides:

[ 3x = \ln(40) - 2 ]

Finally, divide both sides by 3 to solve for (x):

[ x = \frac{\ln(40) - 2}{3} ]

So, (x = \frac{\ln(40) - 2}{3}) is the solution to the equation (14e^{3x+2} = 560).

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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.