Question

michele

Given the parent functions f(x) = log10 x and g(x) = 3x –1, what is f(x) ⋅g(x)?

Answer 1

@Michele_Laino
f(x) ⋅g(x) = log10 x –3x log10 x
check to be right

Answer 2

I think that it is:
\[\Large f\left( x \right) \cdot g\left( x \right) = \left( {{{\log }_{10}}x} \right)\left( {3x - 1} \right)\]

Answer 3

A. f(x) ⋅g(x) = log10 (3x –1)^x
B. f(x) ⋅g(x) = log10 x^(3x –1)
C. f(x) • g(x) = 3x log10 x + log10 x
D. f(x) ⋅g(x) = log10 x –3x log10 x

@Michele_Laino which?

Answer 4

which to be right michele?

Answer 5

yes! If we apply this property of logarithms:
\[\Large m{\log _{10}}n = {\log _{10}}\left( {{n^m}} \right)\]
with n=x, and m=3x-1, we get:
\[\Large f\left( x \right) \cdot g\left( x \right) = \left( {{{\log }_{10}}x} \right)\left( {3x + 1} \right) = {\log _{10}}\left( {{x^{3x + 1}}} \right)\]

Answer 6

is A answer?

Answer 7

A it is not, since we have 3x-1 as exponent, whereas in A we have x as exponent

Answer 8

oh B is right!

Answer 9

that's right!