- #1
guifb99
- 10
- 1
a>b ⇒ Lim(a–b)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b)
b>a ⇒ Lim(b–a)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b)
a∈ℝ
b∈ℝ
c∈ℝ / c>0
b>a ⇒ Lim(b–a)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b)
a∈ℝ
b∈ℝ
c∈ℝ / c>0
Last edited:
guifb99 said:a>b ⇔ Lim(a–b)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b)
b>a ⇔ Lim(b–a)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b)
a∈ℝ
b∈ℝ
c∈ℝ / c>0
I don't see the point of writing this as a limit. Also, when you take a limit, use =, not ≈.guifb99 said:a>b ⇒ Lim(a–b)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b)
b>a ⇒ Lim(b–a)→0 Logc(a+b) ≈ Logc(a) + Logc(√a⋅b)
There are several ways to calculate Log(a+b) without a calculator. One method is to use logarithm rules to rewrite the expression into a more manageable form. For example, Log(a+b) can be rewritten as Log(a) + Log(1+b/a). Another method is to use the Taylor series expansion, which involves using a polynomial approximation to calculate the logarithm. Additionally, there are several online tools and apps available that can quickly and accurately calculate logarithms.
Calculating Log(a+b) is important in various fields of science and mathematics, such as statistics, physics, and engineering. It is often used in calculations involving exponential growth and decay, and in solving equations involving logarithms. Knowing how to calculate logarithms can also help in understanding and interpreting data presented on a logarithmic scale.
Log(a+b) and Log(a) + Log(b) are both expressions involving logarithms, but they are not equivalent. Log(a+b) represents the logarithm of the sum of two numbers, while Log(a) + Log(b) represents the sum of the logarithms of two numbers. In other words, Log(a+b) is a single logarithmic term, while Log(a) + Log(b) is the sum of two separate logarithmic terms.
Yes, Log(a+b) can be negative. This occurs when the sum of a and b is less than 1. In this case, the logarithm of the sum will be a negative number. It is important to note that logarithms of negative numbers or zero are undefined.
One way to check the accuracy of your calculation of Log(a+b) is to use a calculator or online tool to compare the results. Another way is to use logarithm rules to simplify the expression and see if it matches your calculated value. Finally, you can also check if your calculation is reasonable by plugging in values for a and b and verifying if the result is consistent with the properties of logarithms.