Question

i am so lost, when do you use log and when do you use ln? because i just solved 3^2x-1 = 5^x+2 by ln and then i tried solving 3^x-2 = 4^2x+4 but in the answer book, it said to solve by log.....HELP

Answer 1

It is of very little consequence, so long as the context is clear.

A brief history...

1) In algebra and most pre-calculus, the expression log(x) generally means a base 10 logarithm.

2) Logarithms of other bases will normally have the base indicated directly, Base 2, being \(\log_{2}(x)\)

3) The one significant exception is the Base "e" logarithm. It is sufficiently common that it has its own symbol, \(ln(x) = \log_{e}(x)\).

4) However, once you get to calculus, the rules change a little. The base e logarithm becomes so common that base 10 is now the odd duck and the symbol log(x) begins to mean the base e logarithm. As long as the context is clear, no one should care if you use either ln(x) or log(x) to mean the base e logarithm

5) Calculators are a different matter. Since you can't relable the face of the keyboard every other problem, the keys are stamped with log(x) for base 10 and ln(x) for base e.

Really, you just have to get used to it. When in doubt, be specific. If it's not perfectly clear that log(x) means base e, then make it clear by using either ln(x) or \(log_{e}(x)\).

Answer 2

@tkhunny wait so you can use both log and ln in both equations?

Answer 3

Answer 1) Yes, but read my last paragraph again before you run off on your own! :-)

Answer 2) Not at the same time! Stick to one or the other for any given context.

Answer 3) If a base is convenient, use the convenient base. In this case, 3, 5 or 3, 4, there is no particularly convenient base. If it were 2 and 8, that would be a different story - use base 2!