Question: If log_3(9) + log_3(27) = x, what is the value of x?
Options:
2
3
4
5
Correct Answer: 4
Solution:
log_3(9) = 2 and log_3(27) = 3, thus x = 2 + 3 = 5.
If log_3(9) + log_3(27) = x, what is the value of x?
Practice Questions
Q1
If log_3(9) + log_3(27) = x, what is the value of x?
2
3
4
5
Questions & Step-by-Step Solutions
If log_3(9) + log_3(27) = x, what is the value of x?
Step 1: Understand that log_3(9) means 'to what power do we raise 3 to get 9?'
Step 2: Since 3^2 = 9, we find that log_3(9) = 2.
Step 3: Next, understand that log_3(27) means 'to what power do we raise 3 to get 27?'
Step 4: Since 3^3 = 27, we find that log_3(27) = 3.
Step 5: Now, we add the two results together: 2 + 3.
Step 6: Therefore, x = 5.
Logarithmic Properties – Understanding how to evaluate logarithms and apply properties such as log_b(a^n) = n*log_b(a) and log_b(a) + log_b(c) = log_b(a*c).
Base Conversion – Recognizing that 9 and 27 can be expressed as powers of 3, specifically 9 = 3^2 and 27 = 3^3.
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