Question

The number of solutions of the equation $3^{x-1}+5^{x-1}=34$

• A. 1
• B. 2
• C. none of these

Answer 1

The correct option is A 1

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

Thus, the equation has no other solution.