If log_7(49) = x, what is the value of x?

If log_7(49) = x, what is the value of x?

Correct Answer: 2

Step 1: Understand the question. We need to find the value of x in the equation log_7(49) = x.
Step 2: Recall the definition of logarithms. log_b(a) = c means that b^c = a.
Step 3: Identify the base and the number in our case. Here, the base is 7 and the number is 49.
Step 4: Rewrite 49 as a power of 7. We know that 49 = 7^2.
Step 5: Substitute this back into the logarithm. So, log_7(49) becomes log_7(7^2).
Step 6: Use the property of logarithms that states log_b(b^c) = c. Therefore, log_7(7^2) = 2.
Step 7: Conclude that x = 2.

Logarithms – Understanding the relationship between exponents and logarithms, specifically how to express a number as a power of its base.
Exponential Equations – Recognizing that 49 can be rewritten as 7 raised to a power (7^2) to simplify logarithmic expressions.