simplify the following expressionSimplify the following expr

simplify the following expressionSimplify the following expressions. Your answers must be exact and in simplest form.

(a) log12(12^(9x9))

(b) 2log2(1010q)

(c) log6561(3^k)=

(d) 5^7log5^88 log5^7

Solution

a. log₁₂12^-9x-9

= (-9x-9) log₁₂12

=--1(9x+9)*1= -9(x+1)

b. 2log₂(10-10q) =2 log₂10(1-q) =2(log₂10 + log₂(1-q))

c. log₆₅₆₁3^k

log 3^k/log6561 = k log 3/(log 3⁸) = k log3/8 log 3 = k/8

d. 5⁷log5⁸- 8 log5⁷

8*5⁷log 5 - 8*7 log 5

8(5⁷-7)log 5= 624944 log 5