If log_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
Practice Questions
Q1
If log_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
x + y
xy
x - y
x/y
Questions & Step-by-Step Solutions
If log_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
Correct Answer: x + y
Step 1: Understand that log_a(6) can be rewritten using the property of logarithms that states log_a(m * n) = log_a(m) + log_a(n).
Step 2: Identify that 6 can be expressed as the product of 2 and 3, so we can write log_a(6) as log_a(2 * 3).
Step 3: Apply the property from Step 1: log_a(6) = log_a(2) + log_a(3).
Step 4: Substitute the values given in the question: log_a(2) = x and log_a(3) = y.
Step 5: Therefore, log_a(6) = x + y.
Logarithmic Properties – Understanding the properties of logarithms, specifically the product rule which states that log_a(m * n) = log_a(m) + log_a(n).
