SOLUTION: I am stuck on this. Any help will be appreciated. Thanks! If log_a(x)=2, log_a(y)=4, and log_a(z)=6, what is the value of log_a((y^2)/((x^2)√(z)) The listed answers are

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am stuck on this. Any help will be appreciated. Thanks! If log_a(x)=2, log_a(y)=4, and log_a(z)=6, what is the value of log_a((y^2)/((x^2)√(z)) The listed answers are       Log On


   

Question 1028712: I am stuck on this. Any help will be appreciated. Thanks!
If log_a(x)=2, log_a(y)=4, and log_a(z)=6, what is the value of log_a((y^2)/((x^2)√(z))
The listed answers are -2, -1, 0, 1, 2, and 3. Now I know that 'a' is unknown. So I assume that I need to use one of the properties to get an answer like log_a1=0, log_aa=1, etc. Using these I was only able to get it to 3log_a(2/6). Any help will be appreciated.
Found 3 solutions by richard1234, MathTherapy, Natolino1983:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
It will help to review your logarithmic properties (particularly with addition, subtraction) since those come in handy. In particular, and . For example:






Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
I am stuck on this. Any help will be appreciated. Thanks!
If log_a(x)=2, log_a(y)=4, and log_a(z)=6, what is the value of log_a((y^2)/((x^2)√(z))
The listed answers are -2, -1, 0, 1, 2, and 3. Now I know that 'a' is unknown. So I assume that I need to use one of the properties to get an answer like log_a1=0, log_aa=1, etc. Using these I was only able to get it to 3log_a(2/6). Any help will be appreciated.
 

log+%28a%2C+%28y%5E2%29%2F%28%28x%5E2%29+%2A+sqrt%28z%29%29%29 

log+%28a%2C+%28y%5E2%29%29+-+%28log+%28a%2C+%28x%5E2%29%29+%2B+log+%28a%2C+sqrt%28z%29%29%29





2%284%29+-+2%282%29+-+%281%2F2%29+6 = 8 - 4 - 3 = highlight_green%281%29

Answer by Natolino1983(23) About Me  (Show Source):
You can put this solution on YOUR website!
We will use this 3 properties 1)log_a (x×y) = log_a(x) + log_a (y)
2)log_a (x/y) = log_a (x) - log_a(y)
3)log_a(x^y) = y×log_a(x)
Therefore log_a ((y^2/(x^2×sqrt(z)) = log_a(y^2) - (log_a(x^2×sqrt(z)) (p.2)
= log_a(y^2) - (log_a(x^2) +log_a(sqrt(z)) (p.1)
=2×log_a(y) -(2×log_a(x) +log_a(z)/2) (p.3)
Replacing: 2×4 - (2×2 +6/2) =8 - 7 = 1
(Obs: sqrt(z) =z^(1/2) )