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
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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) (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:
 = \log_a (y^2) - \log_a (x^2 \sqrt{z}))
)
)
Answer by MathTherapy(10555) (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.
= 8 - 4 - 3 =
Answer by Natolino1983(23) (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) )
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