If log_a(2) = x and log_a(3) = y, what is log_a(6)?
Practice Questions
Q1
If log_a(2) = x and log_a(3) = y, what is log_a(6)?
x + y
xy
x - y
x/y
Questions & Step-by-Step Solutions
If log_a(2) = x and log_a(3) = y, what is log_a(6)?
Correct Answer: x + y
Step 1: Understand that log_a(6) means we want to find the logarithm of 6 with base 'a'.
Step 2: Recognize that 6 can be expressed as the product of 2 and 3, so we write 6 as 2 * 3.
Step 3: Use the property of logarithms that states log_a(m * n) = log_a(m) + log_a(n).
Step 4: Apply this property to log_a(6): log_a(6) = log_a(2 * 3) = log_a(2) + log_a(3).
Step 5: Substitute the values we know: log_a(2) = x and log_a(3) = y.
Step 6: Therefore, log_a(6) = x + y.
Logarithmic Properties – The question tests the understanding of the properties of logarithms, specifically the product rule which states that log_a(m * n) = log_a(m) + log_a(n).
