If log 3 = A and log 7 = B, find log7 (9) in terms of A and B.

Question

Accepted Answer

Hey, everyone. Welcome back in this problem. We're asked to find log base 23 of 29 in terms of M and N. Ok. And we're told that log tw 23 is M and log of 29 is N. Ok. So let's get started with what we want to find. We wanna find log base 23 of 29. Ok. Now we know log of 23 and we know log of 29. Ok. So let's think about what kind of rules we could apply. Ok. Well, the log property that could help us here is our change of base. Now, let's recall if we have a log base B, some value A, we can use our change of base property to write this as log base C of A divided by log base C of B. Ok. So C has to be the same base. All right. Now, looking at our expression while we have B, the base is 23. Can we have the value A is 29? All right, we're gonna choose the base. The base that we want is just 10. So we're just gonna choose that normal base and we can rewrite log base 23 of 29 using this rule as log of A, which in our case is 29 divided by log of the base B which in our case is 23. OK. So we write rewritten our expression as a log of 29 divided by a log of 23. And using the information we're given in the question, this is just going to be N divided by MS. So that's going to be answered. D I hope this video helped. Thanks everyone for watching. See you in the next one.

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If log 3 = A and log 7 = B, find log7 (9) in terms of A and B.

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