Logarithm question
asked Jan 5 in Other Math Topics by TOBI

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3 Answers

answered Jan 5 by Mathical Level 10 User (55,380 points)

The coefficients of the logs can be introduced into the log arguments, so ½ means square root, 2 means squared. Also, the plus between the terms allows us to multiply the arguments together and minus means divide:

log(√(25/4) ÷ (4/5)^2) * (320/125))=log(5/2 * 25/16 * 320/125)=log(125/32*320/125)=log(10)=1. So the answer is 1.

 

answered Jan 7 by Rod Top Rated User (425,620 points)

½log10(25/4)-2log10(4/5)+log10(320/125)

The rules of logs are:

a.log(x) =log(x^a)  ----------------- I

-log(x) = log(1/x)  ------------------ II

log(a) + log(b) = log(ab)  -------- III

using I, ½log(25/4) = log([25/4]^½) = log(5/2)

​using I & II, -2log(4/5) = -log([4/5]^2) = -log(16/25) = log(25/16)

Adding together these logs, using III,

½log10(25/4)-2log10(4/5)+log10(320/125) = log(5/2) + log(25/16) + log(320/125) = log(5/2*25/16*320/125) = log(10) = log10(10) = 1

Answer: 1

answered Jan 7 by Fermat Level 10 User (62,720 points)

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