SOLUTION: Suppose a\neq 0. Compute log_{8a} 4b if a = 1 and b = 32.

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Question 1209354: Suppose a\neq 0. Compute log_{8a} 4b if a = 1 and b = 32.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

To answer this question, I should know what this writing means 


    log_{8a} 4b


but from the post and from your non-mathematical writing I can not get it. 

These dances with hieroglyphs is not Math.



Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

log%288a%2C%284b%29%29=%28log%28%284b%29%29%29%2F%28log%28%288a%29%29%29 Change of base rule.

log%288a%2C%284b%29%29=%28log%28%284%2A32%29%29%29%2F%28log%28%288%2A1%29%29%29 Plug in a = 1 and b = 32.

log%288a%2C%284b%29%29=%28log%28%28128%29%29%29%2F%28log%28%288%29%29%29

log%288a%2C%284b%29%29=%28log%28%282%5E7%29%29%29%2F%28log%28%282%5E3%29%29%29 Rewrite 128 and 8 as powers of 2.

log%288a%2C%284b%29%29=%287%2Alog%28%282%29%29%29%2F%283%2Alog%28%282%29%29%29 Use the rule log(A^B) = B*log(A)

log%288a%2C%284b%29%29=7%2F3

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Another approach

log%288a%2C%284b%29%29=c

4b+=+%288a%29%5Ec

4%2A32+=+%288%2A1%29%5Ec

128+=+8%5Ec

2%5E7+=+%282%5E3%29%5Ec

2%5E7+=+2%5E%283c%29

7+=+3c Since the bases of the previous equation are equal, the exponents must be equal.

c+=+7%2F3

log%288a%2C%284b%29%29=7%2F3

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Answer: 7/3