Question

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

Answer 1

Answer:

Considering the Product and the Power rule of the Logarithms, they're both equivalent for x >0

Step-by-step explanation:

1) Considering the Product and the Power rule of the Logarithms:

$\\log_{c}(ab)=log_{c}a+log_{c}b$

$\\log_{c}a^{b}=blog_{c}$

2) Therefore we can say that:

$\\f(x) = ln ((x)(x^2 + 1))^{\frac{1}{2}}\\\Rightarrow f(x)=ln (x(x^2 + 1))^{\frac{1}{2}}\Rightarrow f(x)=\frac{1}{2}ln((x)(x^{2} + 1)).\\g(x) = \frac{1}{2}(ln (x) + ln(x^{2} + 1))\Rightarrow g(x)=\frac{1}{2}ln(x(x^2+1))$