I think this explanation might be a little better:

Once you understand what  actually means, you will
find this trivial.
 


is defined as the answer to the question  

"To what power (exponent) must B be raised to give A?"

Examples
 


is defined as the answer to the question  

"To what power (exponent) must 5 be raised to give 25?"

The answer to that is 2, because if 5 is raised to the power of 2,
that will 25.

So we write 


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is defined as the answer to the question  

"To what power (exponent) must 3 be raised to give 81?"

The answer to that is 4, because if 3 is raised to the power of 4,
that will 81.

So we write 

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Now your problem:



is defined as the answer to the question  

"To what exponent must 4 be raised to give 4-.38?"

The answer to that is -.38, because if 4 is raised to the power of -.38,
that will give 4-.38"

So we write 

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In general, we write  because the power to which B must
be raised to give BC is obviously C.
 
Edwin