When I'm doing certain math problems regarding logarithms, often times I see some solutions that use logarithms on both sides, and then raise it to the power of that base in order to "k**l" or to cancel out the logarithms. I'm feeling kinda dumb rn, so why does this work exactly?
+9673 Guest:
Do you know the concept of inverse functions? That works because the exponential function and the corresponding logarithmic function are inverse functions of each other. For instance, \(f(x) = 10^x\) and \(g(x) = f^{-1}(x) = \log_{10}x\) are inverse functions and \(f(x) = 2^x\) and \(g(x) = f^{-1}(x) = \log_{2}x\). A property of inverse functions is that \(f(f^{-1}(x)) = f^{-1}(f(x)) = x\). That means \(\log_{10}(10^x) = x\) and \(10^{\log_{10} x} = x\). That's the mechanism behind how it works.
