MCQ practice · SSC Higher Mathematics Board questions · Chapter 9: Exponential and Logarithmic Function
Which is the inverse function of y = log₅ x?
Think it through first, then pick an option.
- a y = log_x 5
- b y = 5ˣ
- c y = log_x (1/5)
- d y = 5⁻ˣ
Answer and explanation
Correct answer: b y = 5ˣ
If y = log₅ x then x = 5ʸ; so the inverse function is y = 5ˣ.
Why the other options are wrong
- a y = log_x 5: In log_x 5 the base has become x; the inverse function is 5ˣ.
- c y = log_x (1/5): log_x(1/5) is not related; the inverse is 5ˣ.
- d y = 5⁻ˣ: 5⁻ˣ = (1/5)ˣ is the inverse of log_(1/5) x, not of log₅ x.
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