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?
+9675 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)=10x and g(x)=f−1(x)=log10x are inverse functions and f(x)=2x and g(x)=f−1(x)=log2x. A property of inverse functions is that f(f−1(x))=f−1(f(x))=x. That means log10(10x)=x and 10log10x=x. That's the mechanism behind how it works.
