Exams › JEE Main › Maths

Find the number of integral values of x satisfying the equation 5^(log₅(x)) + 4x + 20 = 0.

1. 0
2. 1
3. 2
4. 3

Correct answer: 0

Solution

Since 5^(log₅(x)) = x (requires x > 0), the equation becomes x + 4x + 20 = 0, giving x = -4. But x = -4 is outside the domain (x must be positive), so there are no valid integral solutions.

Related JEE Main Maths questions

• Given that logₐ(3) = p, log_b(3) = p³, log_c(27) = 1/(p² + 1), and log₃[(a² * b⁴) / c⁶] = alpha*p³ + beta*p² + gamma*p + delta, find the value of |alpha + beta + gamma + delta|.
• Evaluate: 6^(log₆(5)) + 3^(log₉(16)).
• Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?

⚔️ Practice JEE Main Maths free + battle 1v1 →