Solve for x in the equation 3^x - 2^x = 65

Answer

The given equation is

We can try integer values for

to find a solution.

.
If

Thus,

is a solution.

Let

.
The derivative of

.
Since

and

are always positive, and

, the derivative

is positive when

is large enough.
When

.
When

Since

for

is an increasing function for

.
Therefore,

is the only solution.

Final Answer: The final answer is

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Solve for x in the equation 3^x - 2^x = 65

Question

Answer

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