Which equation can you use to evaluate log(61,296)? a^6 = 1,296 6^a = 1,296 6a = 1,296
The Correct Answer and Explanation is:
ChatGPT said:
The correct equation to evaluate log₆(1,296) is:
6^a = 1,296
Explanation
To understand why 6^a = 1,296 is the correct equation for evaluating log₆(1,296), let’s first break down what a logarithm means.
The expression log₆(1,296) is asking:
“To what power must we raise 6 in order to get 1,296?”
In general, the logarithmic expression log_b(x) = y is equivalent to the exponential form:
b^y = x
So in this case:
- Base (b) is 6,
- x is 1,296, and
- We’re trying to find the exponent a such that: 6^a = 1,296
Therefore, log₆(1,296) = a, where 6^a = 1,296.
Why the other options are incorrect:
- a^6 = 1,296
- This equation says that a raised to the 6th power equals 1,296.
- This is solving for a, not as an exponent of 6, but as the base.
- So it’s equivalent to solving logₐ(1,296) = 6, which is not the same as log₆(1,296).
- 6a = 1,296
- This is a linear equation, not exponential.
- It represents 6 multiplied by a value a, not 6 raised to the power of a.
- Solving 6a = 1,296 gives a = 216, but 6^216 is astronomically larger than 1,296, so this makes no sense in the context of logarithms.
Final Answer:
✅ 6^a = 1,296 is the correct equation to evaluate log₆(1,296).
