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If \(a = \log_{10} 3\) and \(b = \log_{10} 7\), then find \(\log_7 9\) in terms of a and b.

 Dec 16, 2019
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a  = log10 3

b = log10 7

 

By the  change- of- base theorem we have that   

 

a = log 3 / log 10   =   log 3

b = log 7 / log 10 =   log 7                   [Note that log 10  = 1 ]

 

Also note that 

 

2a  =  2 log103   = log103^2   =  log10 9  = log 9 / log 10   =  log  9

 

So

 

log 7 9  =   log  9  / log 7   =  2a / b 

 

 

cool cool cool  

 Dec 16, 2019

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