Answer :
Here are the answers with detailed explanations for each question:
log₃ 1 = ?
- The logarithm of any number where the result is 1, with the number itself being the base of the logarithm, is always 0. This is because any number raised to the power of 0 is 1. Therefore, the correct answer is option d. 0.
If f(x) = e^(x-1) then f(1) = ?
- To find f(1), substitute x with 1 in the given function: f(1) = e^(1-1) = e^0. Since any non-zero number raised to the power of 0 is 1, f(1) = 1. Therefore, the correct answer is option c. 1.
log₅ 125 = ?
- To solve log₅ 125, we need to find the power to which 5 must be raised to get 125. Since 5³ = 125, the correct answer is option b. 3.
If f(x) = x³ - 7 then f(-2) = ?
- Substitute x with -2 in the given function: f(-2) = (-2)³ - 7 = -8 - 7 = -15. Therefore, the correct answer is option c. -15.
Principal period of cos x is ?
- The principal period of the cosine function, cos(x), is the length of one complete cycle of the function. For cos(x), the period is 2π. Therefore, the correct answer is option b. 2π.