log a/b
In mathematics, “log a/b” refers to the logarithm of b with base a
In mathematics, “log a/b” refers to the logarithm of b with base a. The logarithm function is the inverse of exponentiation. It helps us solve exponent equations and understand the relationship between exponential growth and decay.
To evaluate log a/b, we can use the property of logarithms known as the quotient rule:
log a/b = log a – log b
Here’s how to calculate it step by step:
1. Start with the expression log a/b.
2. Apply the quotient rule: log a/b = log a – log b.
This means we subtract the logarithm of b from the logarithm of a.
3. If you have numerical values for a and b, substitute them into the expression.
4. Use a calculator or logarithm table to calculate the logarithms of a and b.
5. Finally, subtract the logarithm of b from the logarithm of a to get the result.
To better understand this concept, let’s consider an example:
Example: Calculate log 100/10.
1. Start with the expression log 100/10.
2. Apply the quotient rule: log 100/10 = log 100 – log 10.
3. Find the logarithm of 100 and 10:
log 100 = 2 (since 10^2 = 100),
log 10 = 1 (since 10^1 = 10).
4. Substitute these values back into the equation:
log 100/10 = 2 – 1.
5. Simplify the subtraction: 2 – 1 = 1.
Therefore, log 100/10 = 1.
It’s important to note that the base of the logarithm, a, must be positive and not equal to 1. Additionally, the number b must be positive.
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