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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? 

 Mar 16, 2019


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.

 Mar 17, 2019

thanks! I understand now!

Guest Mar 17, 2019

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