Answers

2014-07-15T20:55:04+05:30
Log25base8 can be written as 2/3 log5base2
                                         
                but we kknow that log2base10=1/log5*2base2

                                                            =1/log5base2+1
upon simplification we get log5base2=2.32

there for log25base8=2/3*2.32=1.564
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2014-07-16T12:33:01+05:30
 log_{8}25 = log_{2^3}5^2 =  \frac{2}{3} log_{2} 5

\frac{2}{3} log_{2} 5 =  \frac{2}{3}  \frac{log_{10}5}{log_{10}2}

 = \frac{2}{3}  \frac{log_{10}10 - log_{10}2}{log_{10}2}

Now substitute the value of log_{10}2 = 0.3010

= \frac{2}{3}* \frac{1- 0.3010}{0.3010}

= \frac{2}{3}* \frac{0.699}{0.301}

 = 0.666 * 2.322

= 1.5464

log_{8}25 = 1.5464


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