Note if,Originally Posted bynirva

Then,

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,

---------

Thus given,

Then by the chain rule you have,

Thus,

Next given,

Then,

Thus,

Since their derivative match implies that the function differ by a constant. Thus,

Let , then,

Thus, substituting these values,

Note that,

thus,

Call then, , then,

Using the rule of exponents for logarithms we have,

Thus,

Thus,

Thus,

Note: The reason why if then, is simple. Because,