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So what we have here is we have a log B is 4th 2 plus log B is 4th of 32.
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So to solve this type of problem, what we're going to have to do is, we're going to have to see if we can validate the log width.
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But the problem says not to use a calculator. So it's fine.
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So 4 raised to what number is going to give me 2. Well, that's kind of a tough one.
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Because 4 raised to the first power gives me 4. 4 to the 1 half power, though, will give me 2.
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So I can actually do, you know, 4 to the 1 half power will work.
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And however, we're going to get a little bit trickier here. So this would be 1 half, but I got that.
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But then log means 4 to 32. So 4 to square is 16. 4 cubed, though, is 64.
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So there's not going to be an even number that's going to give me 32, right?
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Well, so I guess I could probably maybe see if I can think about real hard in my head.
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But otherwise, you see I have an addition problem.
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Well, I know I can use my properties logarithm to condense it down to 1 logarithm using multiplication.
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So let's try to see if that helps sound it off.
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Log means 2 of 4 times 2 times 32. And this is going to help us because now I can do 2 times 32, which is 64.
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And as I previously stated, I guess I'm going to use my properties.
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But log means 4 is 64. Now it represents 4 raised to what number gives me, so it's 64.
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Well, we know that answer is going to be 3. Yes.
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So when condensing is logarithm's through that way, we know that our answer by using these properties will give us 3.
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And I didn't use my calculator.