SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws       Log On


   

Question 197009This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Laws of Logarithms
Express as a logarithm of a single number or expression
1 - 3 log base 5 of x This question is from textbook Algebra and Trigonometry Structure and Method book 2

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1-3%2Alog%285%2C%28x%29%29 Start with the given expression.


log%285%2C%285%29%29-3%2Alog%285%2C%28x%29%29 Rewrite "1" as log%285%2C%285%29%29


Note: log%28b%2C%28b%29%29=1 where b%3E1.


log%285%2C%285%29%29-log%285%2C%28x%5E3%29%29 Rewrite the second log using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%285%2C%285%2F%28x%5E3%29%29%29 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


So 1-3%2Alog%285%2C%28x%29%29=log%285%2C%285%2F%28x%5E3%29%29%29 where x%3E0



Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Express as a logarithm of a single number or expression
1 - 3 log base 5 of x
-----------------
1 - log(base5)x^3
---
1 = log(base5)5
---
Substitute to get:
log(base5)5 - log(base5)x^3
Combine:
= log(base5)[5/x^3]
===========================
Cheers,
Stan H.