Basics & LogarithmseasyFree

Basics & Logarithms: Sum Values Satisfying Equation

JEE Maths question with a full step-by-step solution.

Question
Sum of all the values of xx satisfying the equation log⁡17log⁡11(x+11+x)=0\log_{17}\log_{11}(\sqrt{x+11}+\sqrt{x}) = 0 is:
A2525correct
B3636
C171171
D00
Solution
Step 1 Remove the loglog
log⁡11(x+11+x)=170=1  ⟹  x+11+x=11\log_{11}(\sqrt{x+11}+\sqrt{x}) = 17^0 = 1 \implies \sqrt{x+11}+\sqrt{x} = 11
 Step 2: Solve
x+11=11−x  ⟹  x+11=121−22x+x\sqrt{x+11} = 11 - \sqrt{x} \implies x+11 = 121 - 22\sqrt{x} + x
22x=110  ⟹  x=5  ⟹  x=2522\sqrt{x} = 110 \implies \sqrt{x} = 5 \implies x = 25
 This satisfies the original equation, so the sum of all values is 25.
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Basics & Logarithms · easy
If x=∏n=12026nx = \prod_{n=1}^{2026} n, then the value of the expression 11log⁡2x+1log⁡3x+⋯+1log⁡2026x\frac{1}{\dfrac{1}{\log_2 x} + \dfrac{1}{\log_3 x} + \cdots + \dfrac{1}{\log_{2026} x}} is
Basics & Logarithms · easy
Number of integral values of xx satisfying the inequality (34)6x+10−x2<2764\left(\dfrac{3}{4}\right)^{6x+10-x^2} < \dfrac{27}{64} is:
Basics & Logarithms · easy
Number of natural numbers for which the number log⁡4−x(x2−14x+45)\log_{4-x}(x^2-14x+45) is defined is:
Basics & Logarithms · easy
The product of all solutions of the equation e5(log⁡ex)2+3=x8e^{5(\log_{e}x)^{2}+3}=x^{8}, x>0x>0, is

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath