Question

What are the rules of logs to remember for solving for an intensity ratio?

1) Product Rule
2) Quotient Rule
3) Power Rule
4) Change of Base Rule

Answer 1

The rules of logs important for solving an intensity ratio problem in Physics include the Product Rule, Quotient Rule, Power Rule, and Change of Base Rule, which are used to find the difference in sound levels in decibels.

Step-by-step explanation:

The rules of logs crucial for solving intensity ratio problems in Physics, specifically when calculating the difference in sound levels in decibels (dB), include the following:

• Product Rule: The logarithm of a product is the sum of the logarithms of the factors: log(ab) = log(a) + log(b).
• Quotient Rule: The logarithm of a quotient is the difference between the logarithm of the numerator and the denominator: log(a/b) = log(a) - log(b).
• Power Rule: The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(a^n) = n · log(a).
• Change of Base Rule: This rule allows the change of the base of a logarithm: log_b(a) = log_c(a) / log_c(b), where c is any positive number.

When given the ratio of two intensities such as 2 to 1, the difference in their sound levels in decibels can be calculated using the Quotient Rule of logarithms. In Physics, sound intensity levels are measured in decibels using the formula: dB = 10 · log(I1/I2), where I1 and I2 are the intensities.