If log_10(2) = a, what is log_10(20) in terms of a?
Practice Questions
Q1
If log_10(2) = a, what is log_10(20) in terms of a?
2a
a + 1
a + 2
2 + a
Questions & Step-by-Step Solutions
If log_10(2) = a, what is log_10(20) in terms of a?
Step 1: Start with the expression we want to find: log_10(20).
Step 2: Recognize that 20 can be written as 2 multiplied by 10, so we rewrite it: log_10(20) = log_10(2 * 10).
Step 3: Use the property of logarithms that states log_b(m * n) = log_b(m) + log_b(n).
Step 4: Apply this property: log_10(20) = log_10(2) + log_10(10).
Step 5: We know from the question that log_10(2) = a.
Step 6: Also, remember that log_10(10) equals 1 because 10 to the power of 1 is 10.
Step 7: Substitute the values we have: log_10(20) = a + 1.
Logarithmic Properties – Understanding the properties of logarithms, specifically the product rule which states that log_b(m * n) = log_b(m) + log_b(n).
