Question 455075: Hi. My teacher gave me a packet to do for a test next wed and i was wondering if you could help me with a problem.
Solve for x. Give answers to the nearest 100th.
logBASE4(logBASE8(64))=logBASE5(x)
thank you!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve for x. Give answers to the nearest 100th.
logBASE4(logBASE8(64))=logBASE5(x)
thank you!
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The key here is to understand the definition of a logarithm; that is, the base raised to the logarithm of the number=number.
let us look at your problem one part at a time.
logBASE8(64) is asking the question, what do you raise the base(8) to get 64? The answer is 2 because 8^2=64.So, logBASE8(64)=2
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logBASE4(2) is asking the question, what do you raise the base(4) to get 2? The answer is 1/2 because 4^(1/2)=2. so, logBASE4(2)=1/2
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1/2=logBASE5(x) is asking the question, what number do you get when you raise the base(5) to the logarithm of the number(1/2). The answer is √5 because 5^1/2=√5.
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Putting problem back together:
logBASE4(logBASE8(64))=logBASE5(x)
log4(log8(64))=log5(x)
log4(2)=log5(x)
1/2=log5(x)
x=5^(1/2)=√5
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