Question 199819
Given,,,x= log(2a)a,,,,y -log(3a) 2a,,,,z+ log(4a)3a
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to   prove  x*y*z+1 = 2*y*z
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Remember  log(b)x= logx/logb
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loga/log2a * log2a/log3a * log 3a /log4a ) +1 = 2* log 2a/log3a * log 3a/log4a
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reduce  by  eliminating  like  num  and  den
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(loga / log4a) +1  =  2* log2a/log4a
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Remember 2 loga = loga^2,,,,and  a/a =1, loga/loga =1
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(loga/log4a) + log4a/log4a = log (2a)^2 / log 4a
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Remember adding  fractions  with  common  den  ,,,,and   log(a*b) = loga + log b
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(loga +log4a ) / log4a = log 4a^2 / log 4a
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log (a*4a) / log 4a = log 4a^2 /log4a
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log 4a^2 / log 4a = log 4a^2 / log 4a
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To  check,  let  a  = 2,, check  original  and  answer,  all 1 1/3 = 1 1/3 ,,,ok