Well, it seems like you're getting quite logarithmic with these questions! Let me shed some hilarious light on this for you.
So, you want to express log3 5 in terms of a, b, and c. Let's break it down step by step, or should I say logarithm by logarithm?
First, we know that log 3 = b. So, we can rewrite log3 5 as log 3 of 5. Now, we can use the change of base formula to convert it into a more familiar logarithm:
log 3 of 5 = log 5 / log 3.
But what do we do with these fractions? We can't just divide and conquer, can we? Of course, not!
Let's use our friendly logarithmic friends a, b, and c to help us out. log 5 can be expressed as log 2^2 which simplifies to 2log 2, or 2a. Similarly, log 3 can be expressed as log 7 which is simply c.
Now we have:
log 3 of 5 = (2a) / c.
Ah, but we're not done yet! We want to express it in terms of a, b, and c. So, let's replace a and c with their respective logarithmic values:
(2a) / c = (2(log 2)) / (log 7).
But we have one more trick up our sleeve! log 2 can be expressed as log 2 / log 2, or 1. So, we can simplify it further:
(2(log 2)) / (log 7) = (2(1)) / (log 7) = 2 / (log 7).
And there you have it! The expression log3 5 in terms of a, b, and c is 2 / (log 7). Now you can log off and enjoy the beauty of logarithms!