Try the fastest way to create flashcards
Question

# How does $f(x)=\log _{x}(2)$ compare with $g(x)=\log _{2}(x) ?$ Here is one way to find out. a. Use the equation $\log _{a} b=(\ln b) /(\ln a)$ to express f(x) and g(x) in terms of natural logarithms. b. Graph f and g together. Comment on the behavior of f in relation to the signs and values of g.

Solution

Verified
Step 1
1 of 3

a) When we use given equation we can express our functions in this way:

\begin{aligned} f(x)&=\log_x2=\frac{\ln2}{\ln x} \\ \\ g(x)&=\log_2x=\frac{\ln x}{\ln 2} \\ \end{aligned}

## Recommended textbook solutions

#### Thomas' Calculus

14th EditionISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,142 solutions

#### Thomas' Calculus: Early Transcendentals

14th EditionISBN: 9780134439020Christopher E Heil, Joel R. Hass, Maurice D. Weir
12,195 solutions

#### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (6 more)James Stewart
11,085 solutions

#### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927 (1 more)Daniel K. Clegg, James Stewart, Saleem Watson
11,050 solutions