HAT 12/5/16 Name: __________________________________ Advanced Logs Show all work. 1. Without the use of a calculator, compare log 7 51 , log 8 61 , and log 9 71 . Which of these is greatest? Explain your reasoning. 2. Simplify x 3log x 2−log x 5 log a a 2 b. a. log 5 48 − log 5 12 + log 5 4 3log 6 15 − log 6 25 d. c. f. (log 7 5)(log 3 7)(log 2 27)(log 5 2) HINT: Use change of base theorem 3. Solve. 1. log 2 x + log 2 (x − 2) = 3 2
c.) log 4 x 2 = ( log 4 x ) ( )
(
b.) log 2 ( log 3 x ) = 3 d.) log 8 10 − log 8 ( 7 − x ) = log 8 x f.) 9 x − 12 3x = −27 )
e.) log 2 x 2 − 6x = 3 + log 2 (1− x ) ( )
CHALLENGE!! (You will need a separate sheet of paper…) ⎛ a+ b⎞ 1
If !a2 + b2 = 7ab , show that log ⎜
= loga + logb ⎝ 3 ⎟⎠ 2
!
(
)