# How do you solve #(e^(x+5) / e^(5)) = 3#?

Solution:

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On the left side, we have the same bases, so we can subtract the exponents.

We now have the equation

Hope this helps!

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To solve the equation (\frac{{e^{(x+5)}}}{{e^5}} = 3), you can begin by multiplying both sides of the equation by (e^5) to eliminate the denominator:

(e^5 \times \frac{{e^{(x+5)}}}{{e^5}} = 3 \times e^5)

(e^{(x+5)} = 3e^5)

Next, take the natural logarithm (ln) of both sides to solve for (x):

ln((e^{(x+5)})) = ln((3e^5))

(x + 5 = \ln(3e^5))

Now, apply the properties of logarithms to simplify:

(x + 5 = \ln(3) + \ln(e^5))

Remembering that (\ln(e^5) = 5), we have:

(x + 5 = \ln(3) + 5)

Subtract 5 from both sides to isolate (x):

(x = \ln(3))

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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.

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.

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.

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