Question

Write logarithmic expressions in exponential form. ANALYZE Let f(x)=log_(10)(x) and g(x)=10^(x). Find f(g(x)) and g(f(x)) and justify your conclusion.

Answer 1

Logarithmic and exponential forms are inverses. For the given functions, f(x) = log10(x) and g(x) = 10x, when we plug each function into the other, we end up with x. Hence, f(g(x)) = g(f(x)) = x.

Step-by-step explanation:

Remember, logarithmic and exponential forms are inverse of each other. f(x) = log10(x) converts to exponential form as: 10f(x) = x. Similarly, g(x) = 10x converts to logarithmic form as: log10(g(x)) = x.

Now for f(g(x)) and g(f(x)), we substitute the functions: f(g(x)) means that we plug g(x) into f(x), and that gives us log10(10x) which simplifies to x. Now for g(f(x)), we plug f(x) into g(x), which gives us 10log10(x) which also simplifies to x. Hence, for this particular example, f(g(x)) = g(f(x)) = x.

Learn more about Logarithmic and Exponential Forms