- #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
- Thread starter Gughanath
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- Simplify
In summary, The steps to simplify log5/log125 to 1/3 are as follows: first, recognize that 125 can be written as 5^3. Then, use the definition of logarithms to rewrite log5/log125 as log5/log(5^3). Next, simplify the logarithms by canceling out the log(5)s, leaving 1/3 as the final result. It is important to pay attention to the properties of logarithms, as the expression log(a)/log(b) is not equal to log(a/b).
- #2
danne89
- 180
- 0
Which base?
- #3
Gughanath
- 118
- 0
10, sorry for not mentioning that.danne89 said:
- #4
- 13,368
- 3,525
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
- 13,368
- 3,525
[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
- 13,368
- 3,525
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?
FAQ: Steps on how to simplify log5/log125 to 1/3
What does "log5/log125" mean?
"log5/log125" is a mathematical expression that represents the logarithm of 5 divided by the logarithm of 125. Logarithms are mathematical functions that help us solve exponential equations and find unknown values.
Why do we need to simplify "log5/log125" to 1/3?
Simplifying "log5/log125" to 1/3 allows us to easily solve equations and find values without using logarithms. It also helps us better understand the relationship between logarithms and exponents.
What are the steps to simplify "log5/log125" to 1/3?
The steps to simplify "log5/log125" to 1/3 are as follows:
1. Rewrite the logarithms as exponents: log5 = 5^x and log125 = 125^x
2. Substitute the exponent expressions into the original expression: 5^x / 125^x
3. Simplify by dividing the two exponents with the same base: (5/125)^x
4. Simplify the fraction: (1/25)^x
5. Rewrite as a fraction with 1 as the numerator: 1 / (25^x)
6. Since (25^x) = 1/3, substitute the value into the expression: 1 / (1/3)
7. Simplify: 3
Is "log5/log125" equal to 1/3 in all cases?
Yes, "log5/log125" is equal to 1/3 in all cases. This is because logarithms follow certain rules and properties, and when these are applied, the expression will always simplify to 1/3.
What are some real-life applications of simplifying "log5/log125" to 1/3?
Simplifying "log5/log125" to 1/3 can be useful in solving exponential growth and decay problems, calculating pH levels, and analyzing data in fields such as economics, biology, and computer science.