SOLUTION: Please help with this question "Express as a single logarithm and, if possible, simplity." 1. 2/5 log(a)x - 1/3 log(a) y 2. ln 2x + 3(1n x - ln y) Thank you.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help with this question "Express as a single logarithm and, if possible, simplity." 1. 2/5 log(a)x - 1/3 log(a) y 2. ln 2x + 3(1n x - ln y) Thank you.      Log On


   

Question 167904: Please help with this question "Express as a single logarithm and, if possible, simplity."
1. 2/5 log(a)x - 1/3 log(a) y
2. ln 2x + 3(1n x - ln y)
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

1)



Start with the given expression


Rewrite the expression using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29. In other words, take the coefficient that is in front of the logs and place them as exponents



Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


This next step is optional:

Convert from exponent notation to radical notation.


So the answer is (which is in exponent notation) or (which is in radical notation)