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log = logarithm in base 10.

ln = logarithm in base e.

logx = logarithm in base x.

Upon some investigation, I found that log(a)/ln(a)=log(b)/ln(b) where a and b are constants,

meaning that there is a ratio between the logarithms.

What is the function of this ratio, in terms of logx and logy?

I.e. If logy(c)=f(x)logx(c), what is f(x)?

The reason behind my search here is to find out how to put a logx (logarithm in base x) function in terms of ln. I want to experiment with various functions in logx on my graphics calculator, but it doesn't have the option to use logarithms in bases other than e and 10.