JEE Main 2021 · 17 March · morning · Single correct · +4 / −1
The inverse of y = 5ˡᵒᵍˣ is :
- (a) x = 5ˡᵒᵍʸ
- (b) x = y^(1/(log 5))
- (c) x = 5^(1/(log y))
- (d) x = yˡᵒᵍ⁵
Answer and solution
Answer (b) x = y^(1/(log 5))
Solution
Maths sir · 3 steps
Use aˡᵒᵍᵇ = bˡᵒᵍᵃ to turn 5ˡᵒᵍˣ into a power of x, then undo that power.
- Swap base and argument. Take log of 5ˡᵒᵍˣ to get log x · log 5. Take log of xˡᵒᵍ⁵ to get log 5 · log x. These are equal, so 5ˡᵒᵍˣ = xˡᵒᵍ⁵.
y = 5ˡᵒᵍˣ = xˡᵒᵍ⁵
- Undo the power. To get x alone, raise both sides to the power 1/(log 5). This gives y^(1/(log 5)) = x^(log 5 · 1/(log 5)) = x.
- So. The inverse is x = y^(1/(log 5)), which is option (b).
The idea to keep. When the variable sits inside a log in the exponent, rewrite with aˡᵒᵍᵇ = bˡᵒᵍᵃ. A power of x is much easier to invert: just raise to the reciprocal power.
Answer from the NTA final answer key. Solution by PrepWiser.