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Question

The number of solutions of the equation 3x1+5x1=34

A
1
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B
2
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C
none of these
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Solution

The correct option is B 1
It is very obvious that at x = 3 the given expression satisfies. Now, y=3x1 and y=5x1 are both increasing function (exponential functions with base greater than 1). Therefore their sum y=3x1+5x1 is also an increasing function of x. It means for x < 3, y=3x1+5x1 < 34 and for x > 3, y=3x1+5x1 > 34.

Thus, the equation has no other solution.

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