SOLUTION: I am so confused with this problem. Express as a sum, difference, and product of logarithims, without using exponents. 3 log b √ x^8/y^2z^5 I could not get i

Algebra ->  Square-cubic-other-roots -> SOLUTION: I am so confused with this problem. Express as a sum, difference, and product of logarithims, without using exponents. 3 log b √ x^8/y^2z^5 I could not get i      Log On


   

Question 212356: I am so confused with this problem.
Express as a sum, difference, and product of logarithims, without using exponents.
3
log b √ x^8/y^2z^5
I could not get it to show the way the problem does. It reads log (small b below) square root with 3 above the square root symbol. Inside the square root symbol it has x^8 over y^2z^5.


Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Express as a sum, difference, and product of logarithims, without using exponents.
3
log b √ x^8/y^2z^5
I could not get it to show the way the problem does. It reads log (small b below) square root with 3 above the square root symbol. Inside the square root symbol it has x^8 over y^2z^5.
------------------------
log(base b) [x^8/y^2*z^5]^(1/3)
-----
= (1/3){log(b)[x^8] - log(b)[y^2z^5]}
---
= (1/3)[8log(b)x - [2log(b)y + 5log(b)z]}
---
= (8/3)log(b)x - (2/3)log(b)y - (5/3)log(b)z
===================================================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given expression.


... Convert to rational exponent notation.


... Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


... Break up the log using the identity log%28b%2C%28A%2FB%29%29=log%28b%2C%28A%29%29-log%28b%2C%28B%29%29


... Break up the second log using the identity log%28b%2C%28A%2AB%29%29=log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29


Distribute


... Pull down the exponents using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


... Distribute


So




assuming that every variable is positive.