Logarithms

[Math Tutor]

What do you know the logarithms?

Why are they thought?

[dduclam]

What do you know the logarithms?

Why are they thought?

[tex]y=log_ax \Leftrightarrow x=a^y[/tex]

[Guest]

First, any time you have a function, f(x), it's really good to have its inverse function, [tex]f^{-1}[/tex]. It lets you solve the equation f(x)= y: [tex]f^{-1}(f(x))= x= f^{-1}(y)[/tex]. For the function, [tex]f(x)= a^x[/tex], its inverse function is [tex]log_a(x)[/tex], The solution to [tex]a^x= b[/tex] is [tex]x= log_a(b)[/tex].

Also the logarithm has some nice "arithmetic" properties. log(ab)= log(a)+ log(b) and [tex]log(a^b)= blog(a)[/tex].