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

one solution

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two solutions

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three solutions

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four solutions

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Solution

The correct option is A one solution
The total number of solutions are same as the number of points of intersection of the given curves.
$y = 3^{x - 1} + 5^{x - 1}$ and $y = 34$ , as shown in the graph.
It is evident that these two curves intersect at exactly one point.
$∴$ Exactly one solution exists.
Hence, option 'A' is correct.

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