In Exercises 93–102, solve each equation. 3^x2=45

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this equation. 11 raised to the X squared equals 69 we are asked to solve for X. Well, X's way up here in this exponents. How do we solve for it? Well, we recall from previous lessons the power rule which states that the natural log of B raised to the X. Hey look, there's an X in the exponent just like what we have equals X times the natural log of B. Okay, well all we have to do then to bring this X down out of the exponent is put it in front of a natural log but we don't have a natural log over here. Well what do we do? We're going to take the natural log of both sides and then what we'll have is X squared times the natural log of equals the natural log of 69. Okay, this is looking a little bit more doable. Okay, let's divide both sides by the natural log of 11. To get that X squared by itself on the left. So now we'll have X squared equals the natural log of 69 divided by the natural log of 11. And this natural log of 69 natural log of 11. Those are, it's like they're inside parentheses. You can't cancel anything out. You can't cancel out the natural logs, you can't bring that out. You can't factor it. They just have to be done to each one. X squared is very close to being X by itself. Let's get rid of the squared by taking the square root of both sides and so on the left we have X, which is what we want. And on the right we take the square root so it'll be a plus or minus the square root of The natural log of 69 in the numerator, divided by the natural log of 11 in the denominator. And note that because it's plus or minus, there are two solutions. So we look at our answer choices and this matches with answer choice. B. Well done, we'll catch you on the next one.

In Exercises 93–102, solve each equation. 3^x2=45

Key Concepts

Exponential Equations

Logarithms

Change of Base Formula

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