Answer:
[tex]f(x)\cdot g(x)=5x\log_{10} x-2\log_{10} x[/tex]
Step-by-step explanation:
Given : The parent functions [tex]f(x) =\log_{10} x[/tex] and [tex]g(x) = 5x-2[/tex]
To find : What is [tex]f(x)\cdot g(x)[/tex]
Solution :
Expression [tex]f(x)\cdot g(x)[/tex]
Step 1: Substitute the values of f(x) and g(x)
[tex]f(x)\cdot g(x)=\log_{10} x\cdot (5x-2)[/tex]
Step 2: Multiply every element of f(x) with every element of g(x)
[tex]f(x)\cdot g(x)=\log_{10} x(5x)+(\log_{10} x)(-2)[/tex]
Step 3: Simplify and solve
[tex]f(x)\cdot g(x)=5x\log_{10} x-2\log_{10} x[/tex]
