SOLUTION: (1) log3 1/9 (2) log3^3 +log3^9 (3) log6 216=3 (4) log8 4 + log8 16 (5) log12 288- log12 2 (6). Log2 + log5 (7) log10=1 (8) 3^7=2187 (9) 4^p=q (10) X^y=2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: (1) log3 1/9 (2) log3^3 +log3^9 (3) log6 216=3 (4) log8 4 + log8 16 (5) log12 288- log12 2 (6). Log2 + log5 (7) log10=1 (8) 3^7=2187 (9) 4^p=q (10) X^y=2      Log On


   

Question 1153167: (1) log3 1/9
(2) log3^3 +log3^9
(3) log6 216=3
(4) log8 4 + log8 16
(5) log12 288- log12 2
(6). Log2 + log5
(7) log10=1
(8) 3^7=2187
(9) 4^p=q
(10) X^y=2
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

(1)
log%283%2C+1%2F9%29
=log%283%2C+1%29-log%283%2C9%29
=0-2
=-2
(2)
log%283%5E3%29+%2Blog%283%5E9%29
=3log%283%29+%2B9log%283%29
=12log%283%29

(3)
log%286%2C+216%29=3
=log%28+216%29%2Flog%286%29=3
=log%28+216%29=3log%286%29
=log%28+216%29=log%286%5E3%29
=216=6%5E3
=216=216-> true

(4)
log%288+%2C4%29+%2B+log%288+%2C16%29
=log%284%29%2Flog%288%29+%2B+log%2816%29%2Flog%288%29
=log%282%5E2%29%2Flog%282%5E3%29+%2B+log%282%5E4%29%2Flog%282%5E3%29
=%282log%282%29+%2B4+log%282%29%29%2F3log%282%29
=%286+log%282%29%29%2F3log%282%29
=%28cross%286%292+cross%28log%282%29%29%29%2Fcross%283%29cross%28log%282%29%29
=2
(5)
log%2812%2C+288%29-+log%2812%2C+2%29
=log%28288%29%2Flog%2812%29-+log%282%29%2Flog%2812%29
=%28log%28288%29-+log%282%29%29%2Flog%2812%29........log%28288%29=log%282%5E5%2A3%5E3%29=5log%282%29+%2B+2+log%283%29 and log%2812%29=log%282%5E2%2A3%29=2log%282%29+%2B++log%283%29
=%285log%282%29+%2B+2log%283%29-+log%282%29%29%2F%282log%282%29+%2B++log%283%29%29
=%284log%282%29+%2B+2log%283%29%29%2F%282log%282%29+%2B++log%283%29%29
=2%282log%282%29+%2B+log%283%29%29%2F%282log%282%29+%2B++log%283%29%29
=2cross%28%282log%282%29+%2B+log%283%29%29%29%2Fcross%28%282log%282%29+%2B++log%283%29%29%29
=2

(6).
log%282+%29%2B+log%285%29
=log%282%2A5%29
=log%2810%29
=1

(7)
log%2810%2C10%29=1
log%2810%29%2Flog%2810%29=1
1=1
(8)
3%5E7=2187
3%2A3%2A3%2A3%2A3%2A3%2A3=2187
2187=2187
(9)
4%5Ep=q
log%284%5Ep%29=log%28q%29
p%2Alog%284%29=log%28q%29
p=log%28q%29%2Flog%282%5E2%29
p=log%28q%29%2F2log%282%29
(10)
x%5Ey=2
log%28x%5Ey%29=log%282%29
y%2Alog%28x%29=log%282%29
y=log%282%29%2Flog%28x%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
(1) log3 1/9
(2) log3^3 +log3^9
(3) log6 216=3
(4) log8 4 + log8 16
(5) log12 288- log12 2
(6). Log2 + log5
(7) log10=1
(8) 3^7=2187
(9) 4^p=q
(10) X^y=2
I'm doing just 1 for you. I shouldn't have, considering that:

1) not 1 question was posed

2) you shouldn't have posted so many problems

3) I feel so sorry for you having to look at and trying to follow that MOST COMPLICATED simplification that woman

   posted - I wish she'd try to LEARN how to really help these people who ask for help, instead of filling them with MATH ANXIETY. 

Therefore, I'll do # 5.



A "word of advice": Number 4 is done the same way as the above!