{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW6 Sol - Math 2312 Homework 6 1 Solve the equation Give an...

This preview shows pages 1–3. Sign up to view the full content.

Page 1 of 10 Math 2312 Homework 6 1. Solve the equation. Give an exact answer. 2 ) 8 ( log log 3 3 x x Solution: 1 , 9 0 ) 1 )( 9 ( 0 9 8 9 8 log 3 ) 8 ( ) log( log log 2 ) 8 ( log 2 2 2 3 x x x x x x x x b a c b x x ab b a x x c a where we applied a log property in line one (the sum of logs is a log of a product) and we converted the log equation into an exponential equation in line 2. We also note that x = -1 is not in the domain of x 3 log and ) 8 ( log 3 x in the original equation, so the only solution for the original equation is x = 9. 2. If x x f ln ) ( use properties of logarithms to show that h x h h x f h x f 1 1 ln ) ( ) ( Solution: a h b b a x h x x h x h b a b a h x h x h x h x h x f h x f log log ln ln 1 log log log ln ln ) ln( ) ( ) ( 1 In the second line we applied the property that a difference in logs is the log of a quotient, and in the last line we applied the property that a number times a log is equivalent to placing the number in the exponent of the function inside the log.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Page 2 of 10 3. Given x x x f ln ) ( and x e x g 2 ) ( , find, and simplify a) )) ( ( x g f Solution: Replacing x in f(x) with empty parentheses, ) ( ln ) ( ) ( f then x e x x f f e e a a e e e e e e e e x g x g x g f x x x bc c b x x x x x x x x 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2 )) ( ( ln ln ln ln ) ( ln ) ( ) ) ( ( ln )) ( ( )) ( ( In the last line, we applied the property x x f f )) ( ( 1 b) )) ( ( x f g Solution: The outer function is now g(x), so we replace all x in g(x) with empty parentheses: ) ( 2 ) ( e g so x x x x a x x x x c b c b x x x x x x x f xe x x f f x e e e b a b e e e e a a a e e e e e x f g 2 1 2 ln 2 ln 2 1 2 2 ln 2 2 ln 2 2 ln 2 2 ) ln ( 2 ) ) ( ( 2 )) ( ( log log ) ) ( ( 2 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}