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OpenStudy (anonymous):
If the geometric mean of two +ve numbers a and b is 100, then the arithmetric mean of loga and logb is...? I think the answer is 2, am i correct? @shubhamsrg
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OpenStudy (shubhamsrg):
well assuming base of your log is 10, yes 2 seesm right
OpenStudy (shubhamsrg):
seems*
OpenStudy (anonymous):
thx
OpenStudy (phi):
geometric mean of two numbers a and b = 100 means \[ \sqrt{a b} = 100 \\ ab= 10^4\] take the log base 10 of both sides: \[ \log(ab) = log(10^4) \\ log(a)+log(b)= 4 \] the mean of log(a)+log(b) is ( log(a)+log(b))/2 = 4/2 = 2
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