The value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1
What is the Law of Base change in Logarithm ?
According to the law of base change
[tex]\rm \log _b a = \dfrac{ log _d b}{log_d a}[/tex]
The given expression is
[tex]\rm { log _3 5}\times{log_{25} 9}[/tex]
This can be written as
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 9 }{log_{10} 3*log _{10}25}[/tex]
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 3^2 }{log_{10} 3*log _{10}5^2}[/tex]
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *2log _{10} 3 }{log_{10} 3* 2 log _{10}5}[/tex]
On solving this the value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1
To know more about Logarithm law
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