SOLUTION: log(b)squareroot((x^6y^2)/(z^5)) Write the expression in expanded form. I know that the answer is 3log(b)x+log(b)y-(5/2)log(b)z but please explain. Thanks!

Question 1000710: log(b)squareroot((x^6y^2)/(z^5))
Write the expression in expanded form.
I know that the answer is 3log(b)x+log(b)y-(5/2)log(b)z
but please explain.
Thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
log(b)squareroot((x^6y^2)/(z^5))
Write the expression in expanded form.
-------
logb[x^6*y^2)/z^5]^(1/2)
-----
= (1/2)[6logb(x)+2logb(y)-5logb(z)]
============
= 3*logb(x) + logb(y) - (5/2)logb(z)
-------------
Cheers,
Stan H.
-------------
RELATED QUESTIONS
is this true or false: 3log(b)√3:(a)=log[b](a) assume that x,y,z are positive... (answered by Edwin McCravy)

Assume that x,y,z and b are positive numbers. Use the properties of logarithms to write... (answered by jim_thompson5910)

Write the following as single logarithm: 1) 3log(x-1)-2log(x)+5log(x^2)-log(x+1) 2)... (answered by Edwin McCravy)

Write as a single logarithm a) 2 log 5 log b b) 3 log x + 1/2 log y c) 2 log m + log n (answered by lwsshak3)

Write in expanded form: log b [on the bottom] ((x^3y^2)/sqrt(w)) (answered by ewatrrr,stanbon)

Write the expression in condensed form. (1/2)log(a)x+3log(a)y-4log(a)x I know that the... (answered by stanbon)

Let a= log x, b = log y and c = log z Write log (x^2 root y/z^3) in terms of a, b and c (answered by jim_thompson5910)

my earlier submission looks to be jumbled. I have tried to put the same questions in a... (answered by CharlesG2)

Assume that x, y, z, and b are positive numbers. Use the properties of logarithms to... (answered by josgarithmetic)