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General Solution of Trigonometric Equation

The equation ...

Question

The equation $3^{x - 1} + 5^{x - 1} = 34$ has

one solution

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two solution

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no solution

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three solution

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Solution

The correct option is A one solution
The number of solutions is same as the number of points of intersection of the curves
$y = f (x) = 3^{x - 1} + 5^{x - 1}$ and $y = 34$

$y = 3^{x - 1} + 5^{x - 1}$ is a strictly increasing function.
Hence, the number of solution is $1.$

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