Respuesta :

hello

f(x) · g(x) = f·g(x) = (log x)(5x-2) = 5x(logx) -2logx

I changed log base 10 to just log for simplicity.

Have a nice day :D

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]