SOLUTION: Question about logarithms: log₃ 16 - 2log₃ 36 log₃(16) - 2log₃(36) = log₃(16) - log₃(36²) = log₃(16/36²) = log₃(1/81) =

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Question about logarithms: log₃ 16 - 2log₃ 36 log₃(16) - 2log₃(36) = log₃(16) - log₃(36²) = log₃(16/36²) = log₃(1/81) =      Log On


   

Question 915683: Question about logarithms:
log₃ 16 - 2log₃ 36
log₃(16) - 2log₃(36) = log₃(16) - log₃(36²)
= log₃(16/36²)
= log₃(1/81)
= log₃(3⁻⁴)
= -4
Why is the answer 4? as I see it would go at 16/36^2 to 4/9^2 then 4/81 where does the -4 answer come from if this is correct to begin with.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Your steps are not very efficient, but they ARE CORRECT. Your result of -4 is also correct. You seem confused right about the middle:

16%2F%2836%5E2%29

%284%2A4%29%2F%284%2A9%2A4%2A9%29

1%2F%289%2A9%29

1%2F81

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!
Question about logarithms:
log₃ 16 - 2log₃ 36
log₃(16) - 2log₃(36) = log₃(16) - log₃(36²)
= log₃(16/36²)
= log₃(1/81)
= log₃(3⁻⁴)
= -4
Why is the answer 4? as I see it would go at 16/36^2 to 4/9^2 then 4/81 where does the -4 answer come from if this is correct to begin with.


The answer is NOT 4, but - 4, instead. I guess you meant, "Why is the answer - 4?"

16%2F36%5E2 = 16%2F1296 = 1%2F81.

Since 1%2F81 = 3%5E-+4, this results in: log+%283%2C+3%5E-+4%29, which means that:

3%5Ex+=+3%5E-+4

highlight_green%28highlight_green%28x+=+-+4%29%29 ------- Bases are equal and so are their expenents