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Need help with this logs question.?
Log(base 2)x + Log(base 3)x = 1
I know it is a change of base problem (rule 8) but because the bases are primes I'm stuck. Any help would be greatly appreciated
1 Answer
- ?Lv 77 years agoFavourite answer
There is a property where logs can be converted to natural logs regardless of whatever base
If you have log (base y) x where x and y are reals, then
log (base y) x = (ln x) / ln(y)
so you can rewrite this as
[ ln(x) / (ln 2) ] + [ ln(x) / ln(3) ] = 1
ln(x) (( 1 / ln(2) + 1 /(ln 3)) = 1
1 / ln(x) = [ 1 / ln(2) + 1 /(ln 3) ]
taking reciprocal of both sides,
ln(x) = [ 1 / ln(2) + 1 /(ln 3) ]
x = exp ( [ 1 / ln(2) + 1 /(ln 3) ] ^(-1) )
x = 1.53
