Solve each exponential equation in Exercises 1–22 by expressing e...

Question

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^2x−1=32

Accepted Answer

Everyone in this problem. We are asked to solve the following exponential equations by first converting the terms into the same bases and were given 5 to the three X -4 is equal to 3125. Alright so rewriting what we're given, We know five is prime so it can't be broken down any further. So the base on the left hand side is going to stay as five. We're gonna want to convert that 3,125 into something with base five. Well that's a big number so we might not recall right away Which exponents gonna do that for us. So we can build it up. We know that five. The exponent one is 5 and five squared is 25 five. Cute. Well that's gonna be five squared times five. That's 25 times five. Just going to be 125. Well 5 to the four that can be broken down as five cute times five. Well we know five cube is Multiplying by five. Again we get 625. Five to the five similarly is going to be five to the four times five And this one finally is going to be 625 times five which gives us 3,125. That number we were looking for. Okay so if you can't recall the exponents, what you can do is you can build it up term by term with just a simple multiplication. Okay the way we've done it we just need to multiply by five each time. Which is something that you can do even if you don't have a calculator with you. Okay so rewriting our equation, we have five to the three X minus four. It's going to equal five to the exponent five. Alright now we have terms. They are equal and the bases are the same. Well that means that the exponents must be the same. So we can set the exponents equal to each other. And so for X three x minus four is equal to five. Moving the four to the right hand side gives us three X equals 29. And finally dividing by three, we have X equals to three. There's our answer. That's answer. C. I hope this helped. Thanks for watching everyone.

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Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^2x−1=32