Question

Verifying Properties of logarithms In Exercise,use a graphing utility to verify that the functions are equivalent for x > 0.

f(x) = Inx^2/4
g(x) = 2 In x - In 4

Answer 1

what she said

Explanation:

Answer 2

Applying Quotient and power rule. Graphically, for x>0 both curves coincide.

Explanation:

1) Firstly, by applying the Quotient and then the Power Rule, we have a subtraction of the argument and, finally the exponent turns to be the coefficient. As it follows:

`lnx=log_(e)x\\\\f(x) = ln({(x^(2))/(4)})\Rightarrow f(x)=ln{x^2}-ln4\Rightarrow f(x)=2lnx-ln4\\g(x) = 2 ln x - ln 4`

2) Check the graph below to see this equivalence. to see x>0 they both coincide.