Note if,Originally Posted by nirva
for sum real number .
This is the method which I presume your teacher wants you to prove this.
I am going to find the derivatives of these two function. Notice that,
Then by the chain rule you have,
Since their derivative match implies that the function differ by a constant. Thus,
Let , then,
Thus, substituting these values,
Call then, , then,
Using the rule of exponents for logarithms we have,
Note: The reason why if then, is simple. Because,