Please solve question number 18
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logarithm of a with base b=log(a)/log(b).
log(n)/log(a) - log(n)/log(b) / log(n)/log(b)-log(n)/log(c)
=> log(n) (1/log(a) -1/log(b)) /log(n) ( 1/log(b) - 1/ log(c) )
=> log(a)-log(b)/ log(a)log(b) / log(b)-log(c) / log(b)log(c) => log(a/b) /log(a)log(b) × log(b)log(c)/log(b/c) => log(c)/log(a) × log(a/b) / log(b/c)
if b=√ac=> b^2 =ac take the anti log of b^2=ac =>
log(b^2) =log(ac) =2log(b) = log(a) +log(c) => log(b)-log(a) = log(c)-log(b) => log(b/a) =log(c/b) so what is left is log(c)/log(a) =log(c)/ log(n)/ log(a)/log(n) =log(n)/log(a) / log(n)/log(c) = logarithm of n with base a/ logarithm of n with base b. Hope it helps you ...
log(n)/log(a) - log(n)/log(b) / log(n)/log(b)-log(n)/log(c)
=> log(n) (1/log(a) -1/log(b)) /log(n) ( 1/log(b) - 1/ log(c) )
=> log(a)-log(b)/ log(a)log(b) / log(b)-log(c) / log(b)log(c) => log(a/b) /log(a)log(b) × log(b)log(c)/log(b/c) => log(c)/log(a) × log(a/b) / log(b/c)
if b=√ac=> b^2 =ac take the anti log of b^2=ac =>
log(b^2) =log(ac) =2log(b) = log(a) +log(c) => log(b)-log(a) = log(c)-log(b) => log(b/a) =log(c/b) so what is left is log(c)/log(a) =log(c)/ log(n)/ log(a)/log(n) =log(n)/log(a) / log(n)/log(c) = logarithm of n with base a/ logarithm of n with base b. Hope it helps you ...
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