SOLUTION: Hello, and before asking i want to just say that you for your help. The question i have is i am asked to write two logarithms as sums and/or differences of logarithms and simplify.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, and before asking i want to just say that you for your help. The question i have is i am asked to write two logarithms as sums and/or differences of logarithms and simplify.      Log On


   

Question 863304: Hello, and before asking i want to just say that you for your help. The question i have is i am asked to write two logarithms as sums and/or differences of logarithms and simplify. The 2 problems i am given are a) log base 3 then in parentheses (x+3/y) all raised to the 6th power. ( hope i said that correctly) and b) is ln(e^3 times x^5/y^7 times square root of z) Thank you for your help and hopefully i was able to explain that correctly.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
write two logarithms as sums and/or differences of logarithms and simplify.
The 2 problems i am given are a) log base 3 then in parentheses (x+3/y) all raised to the 6th power.
Assume the expression is :
log%283%2C%28%28%28x%2B3%29%2Fy%29%5E6%29%29
The log equiv of exponents, both numerator and denominator to the 6th power
6log%283%2C%28%28x%2B3%29%2Fy%29%29 = 6log%283%2C%28x%2B3%29%29 - 6log%283%2C%28y%29%29
:
b) is ln(e^3 times x^5/y^7 times square root of z)
Assume the problem is:
ln%28%28e%5E3%2Ax%5E5%29%2F%28y%5E7%2Asqrt%28z%29%29%29 = ln%28e%5E3%2Ax%5E5%29 - ln%28y%5E7%2Asqrt%28z%29%29
However, we know that the ln of e^3 is 3 therefore we could write it
the square root can be written as an exponent of 1/2
3+%2B+ln%28x%5E5%29 - 7ln%28y%29- 1%2F2ln%28z%29