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Find how many solutions are there in 2^x+3^x+4^x-5^x=0
Find how many solutions are there in 2^x+3^x+4^x-5^x=0

```
2 years ago

Arun
25768 Points
```							one solution.let f(x) = 5^xg(x) = 2^x+3^x+4^xthe exponential functions are monotonic. sum of monotonic functions is monotonic.for x=0 we have f(0) = 1g(0) = 3 g(x) is above f(x) for x=3f(3) = 125g(3) = 8+27+64 = 99f(3) is above g(3)Hence there exists a cross over point in (0,3).
```
2 years ago
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### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions