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How do you solve #3-4e^x=-1#?

Answer 1

Anna Allen

#x=0#

#3-4e^x=-1# can be written as

#4e^x=3+1=4#

or #e^x=1#

and #x=ln1=0#

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Answer 2

Elijah Allen

To solve the equation (3 - 4e^x = -1), follow these steps:

Add 1 to both sides of the equation: (3 - 4e^x + 1 = -1 + 1) (3 - 4e^x + 1 = 0)
Combine like terms: (4 - 4e^x = 0)
Subtract 4 from both sides of the equation: (4 - 4 - 4e^x = 0 - 4) (-4e^x = -4)
Divide both sides of the equation by -4: (\frac{-4e^x}{-4} = \frac{-4}{-4}) (e^x = 1)
Take the natural logarithm (ln) of both sides: (\ln(e^x) = \ln(1)) (x = \ln(1))
Recall that (\ln(1) = 0), so the solution is: (x = 0)

Therefore, the solution to the equation (3 - 4e^x = -1) is (x = 0).

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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.