If logx5=a and log20x=b then find the value of logx10.
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Solution
we know log a to base b is loga/logb so from que we can write a=(log5/logx) b=(logx/log20) therefore 1/b=(log20/logx) a+(1/b)=(log5+log20)/logx (ab+1)/b=log(100)/logx //loga+logb=log(ab) (ab+1)/b=2log(10)/logx //log(x^2)=2logx taking 2 to lhs (ab+1)/2b=log10/logx that is log10 to base x=(ab+1)/2b.....