Exponential Problems

Question

Solve equations algebraically. Approximate the result to three decimals.

a. e^x = e^{x^2 - 2}

b. 7 - 2e^x = 5

Answer 1

First question:

Notice the base of the exponents are both e.

Therefore, you can just set the powers of the two exponents equal to each other.

x = x² - 2

I hope you can solve this.

If not, please leave a comment.

Second question:

You must isolate the exponent, so let's start off by subtracting 7 to both sides.

-2e^x = -2

Now, divide both sides by 2 to isolate even further.

e^x = 1

Lastly, we want to 'bring down" the x from the exponent, so we will take the logarithm base e (ie ln) of both sides.

x = ln(1)

Since ln(1) = 0, we have

x = 0

*Please feel free to ask me any question for clarification.