SOLUTION: Let log base a x= -5, log base a y =2 and log base a z=0.25. determine the values of the following a.) log base a (xy^2/z^3)^2 b.) log base a √x√y√z

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Let log base a x= -5, log base a y =2 and log base a z=0.25. determine the values of the following a.) log base a (xy^2/z^3)^2 b.) log base a √x√y√z      Log On


   

Question 1002151: Let log base a x= -5, log base a y =2 and log base a z=0.25. determine the values of the following
a.) log base a (xy^2/z^3)^2
b.) log base a √x√y√z
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let
log%28a%2C+x%29=+-5,
log%28+a+%2Cy%29+=2 and
+log+%28+a%2C+z%29=0.25
determine the values of the following
a.)
log+%28a%2C%28%28xy%5E2%2Fz%5E3%29%5E2%29%29

log+%28a%2C%28x%5E2y%5E4%2Fz%5E6%29%29

log+%28a%2C%28x%5E2y%5E4%29%29-log+%28+a%2C%28z%5E6%29%29

log+%28a%2Cx%5E2%29%2Blog+%28+a%2Cy%5E4%29-6log+%28+a%2Cz%29

2log+%28+a%2C+x%29%2B4log+%28+a%2Cy%29-6log+%28+a%2Cz%29....substitute given values

2%28-5%29%2B4%2A2-6%2A0.25

-10%2B8-1.5

-3.5


b.)

log%28+a+%2Csqrt%28x%29%2Asqrt%28y%29%2Asqrt%28z+%29%29

log%28+a+%2Csqrt%28x%29%29%2Blog%28+a+%2Csqrt%28y%29%29%2Blog%28+a+%2Csqrt%28z+%29%29



%281%2F2%29log%28+a+%2Cx%29%2B%281%2F2%29log%28+a+%2Cy%29%2B%281%2F2%29log%28+a+%2Cz%29

%281%2F2%29%28+-5%29%2B%281%2F2%29%2A2%2B%281%2F2%29%2A0.25

-2.5%2B1%2B0.125

-1.375