- #1
Gughanath
- 118
- 0
could someone show me the steps on how to simplify log5/log125 to 1/3. I can't do it
Steps on how to simplify log5/log125 to 1/3
- Context: High School
- Thread starter Gughanath
- Start date
-
- Tags
- Simplify
Click For Summary
Discussion Overview
The discussion revolves around the simplification of the expression log5/log125 to the value 1/3, specifically using base 10 logarithms. Participants explore various steps and properties of logarithms to arrive at this simplification.
Discussion Character
- Homework-related
- Mathematical reasoning
Main Points Raised
- One participant requests assistance in simplifying log5/log125.
- Another participant asks for clarification on the logarithm base being used.
- It is noted that the base does not matter as long as it is consistent.
- One participant suggests using the property of logarithms related to powers, indicating that 125 can be expressed as 5^3.
- A participant proposes that log5/log125 can be simplified by recognizing that log5(125) equals 3 and log5(5) equals 1.
- Another participant cautions that the general property \(\frac{\log a}{\log b} \neq \log\frac{a}{b}\) should be kept in mind during simplification.
- It is pointed out that log(125) can be rewritten as 3log(5), leading to the simplification of log5/log125 to log5/(3log5).
- Finally, participants confirm that the log5 terms cancel, resulting in the final expression of 1/3.
Areas of Agreement / Disagreement
Participants generally agree on the steps to simplify the expression, though there are some clarifications and corrections made regarding the properties of logarithms. The discussion does not present any significant disagreements, but rather a refinement of understanding.
Contextual Notes
Some assumptions about logarithmic properties and the handling of bases are discussed, but not all steps are fully resolved or detailed in the conversation.
- #2
danne89
- 180
- 0
Which base?
- #3
Gughanath
- 118
- 0
10, sorry for not mentioning that.danne89 said:
- #4
dextercioby
Science Advisor
- 13,412
- 4,212
It doesn't matter the base,as long it is the same...
Daniel.
Daniel.
- #5
Gughanath
- 118
- 0
yes, so how could I simplify it?
- #6
dextercioby
Science Advisor
- 13,412
- 4,212
[itex]125=5^{3}[/itex] and use one definitory property of the logarithm...
Daniel.
Daniel.
- #7
Gughanath
- 118
- 0
hmmm...that comes to log5 to the power -2?
- #8
danne89
- 180
- 0
Why don't just: log5 125 = 3 and log5 5 = 1 and then just replace log 5 / log 125 = 1 / 3 ??
- #9
dextercioby
Science Advisor
- 13,412
- 4,212
No,remember that in general:
[tex]\frac{\log a}{\log b}\neq \log\frac{a}{b}[/tex]
So pay attention to what u do.
Daniel.
[tex]\frac{\log a}{\log b}\neq \log\frac{a}{b}[/tex]
So pay attention to what u do.
Daniel.
- #10
gerben
- 511
- 1
log(125) = log(53) = 3log(5)
- #11
Gughanath
- 118
- 0
oh right. My bad. so log5/log125 = log5/log5^3 = log5/3log5, the log5's cancel, leaving 1/3. Thanx
- #12
danne89
- 180
- 0
And then cancel out the log(5)s, leaving 1/3?
Similar threads
- · Replies 7 ·
- · Replies 5 ·
- · Replies 5 ·
High School
How does r∪(-p∩q∩-r) simplify to r∪(-p∩q) ?
- · Replies 3 ·
- · Replies 4 ·
- · Replies 6 ·
High School
Straightforward integration…
- · Replies 27 ·
- · Replies 4 ·
High School
Missing out on intermediate algebraic steps
- · Replies 23 ·