Answer each of the following. Between what two consecutive integers must log_2 12 lie?

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Hello, everybody. I'm doing all right today. Today we're gonna be looking at this math question that's asking us which of the given pairs of consecutive integers has log base three of 100 and 21 in between. And the answers provided are a two and three B three and four C four and five N D five and six. Now when I see a, an equation like this, let's say log log base three of 100 and 21 and they're trying to solve, we're trying to, we're trying to solve for the answer of this by basically estimating, where does it fall in between between two and 33 and four and such? So to get kind of like an estimate, I'll set this equal to X where I can solve for X and see where X falls is it in between which two numbers X will fall. So once I set it equal to X, I can rewrite this equation as instead of a logarithm logarithmic equation as an exponential equation. And I can do that by recalling the general formula of how to rewrite that. So I'll write the general formula, let's say we have log of base B of A equal to C that can be rewritten as B to the power C equal to A. So when comparing that to the equation that we have, our base three will be the B in our recall, the 121 will be the A in our recall and the X will be the C in our recall. So using that information, let's rewrite this as an expansion equation. So we'll have three to the power X equals 100 and 21. So now it's just kind of plugging in and see what works and what doesn't. So let's plug in the numbers that we have. We know that three squared. If X was a two is nine three, cubed is three to the fourth power is and three to the fifth, power is and we can stop here. We don't have to try six because we have that three to the fourth power is 81 and 81 is less than 100 and 21 but 100 and 21 is less than three to the fifth power, which is 243. So if X was four, we would get 81 if X was five, we would get 243 and 100 and 21 falls in between those two numbers. Therefore, our value for X is gonna be or, or the pairs of consecutive integers will be four and five in between those two integers is where the log base three of 100 and 21 will fall. So that will be the answer for this question or answer choice. C in this case. So I hope that was helpful. And until next time.

Answer each of the following. Between what two consecutive integers must log_2 12 lie?

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Key Concepts

Logarithms

Base of a Logarithm

Estimating Logarithms