Logarithms - where does the coefficients come from

In summary, to solve for 3log(base5)2 - (1/2)log(base5)9, you can rewrite the second part as -log(base5)3 and take the square root of 9. Then, do the same for 2^3 to get 8. This will give you log(base5)8 - log(base5)3, which can then be simplified further. Remember to divide the second part by the first and to take into account the coefficients when simplifying.
  • #1
weeman203
5
0
for example
3 log (base5) 2 - (1/2)log (base5) 9

how would someone come to work this out
i know that you are suppose to divide the 2nd part by the 1st
but I am not sure where does the coefficients come in
would that mean you multpily the coefficients
 
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  • #2
rewrite the second one so that it is - log (base5) 3
taking the square root of 9
do the same for 2^3 so that it is now 8
log (B5) 8 - log (B5) 3
 
  • #3
jonnhannah said:
rewrite the second one so that it is - log (base5) 3
taking the square root of 9
do the same for 2^3 so that it is now 8
log (B5) 8 - log (B5) 3


OH yeah, now i remember thanks =D
 

Related to Logarithms - where does the coefficients come from

1. What are logarithms and what do they represent?

Logarithms are mathematical functions that represent the power to which a base number must be raised to equal a given number. In other words, they are the inverse operation of exponentiation and help us solve exponential equations.

2. Where do the coefficients in logarithms come from?

The coefficients in logarithms come from the concept of a logarithmic scale, which is used to represent large ranges of numbers in a more manageable way. The coefficients, also known as the base, determine the rate at which the logarithm grows and are typically chosen to be common numbers like 10 or e.

3. How are logarithms calculated?

To calculate a logarithm, we use the formula logb(x) = y, where b is the base, x is the number we are taking the logarithm of, and y is the exponent or power. For example, log10(100) = 2, since 102 = 100.

4. What are some real-life applications of logarithms?

Logarithms are used in many fields, including mathematics, physics, biology, finance, and computer science. Some real-life applications include measuring the acidity of a substance (pH scale), calculating earthquake magnitudes, and analyzing interest rates in compound interest.

5. Is there a limit to how large or small a logarithm can be?

Technically, there is no limit to how large or small a logarithm can be. However, as the base approaches infinity, the logarithm approaches infinity as well. Similarly, as the base approaches 0, the logarithm approaches negative infinity. In practical terms, logarithms are typically used to represent numbers within a certain range, such as 10-10 to 1010.

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