What is the smallest integer n for which 16n = 412?

6. First convert 16 n to the same base 4. You know 16 = 4 x 4 = 4 2 , so you can write 16 n = (16) n = (4 2 ) n = 4 2n . We know that given 16 n = 4 12 , so we can write 4 2n = 4 12 Since both have ase 4, their powers are equal 2n = 12, or n = 6. Key takeaway: When solving problems involving exponents, base is to be seen carefully. It is easy to simplify, as long as they have the same base. Remember following simple formulae:a m x a n = a m+n , a m / a n = a m-n , (a m ) n = a m x n , (a m ) 1/n = a m/ n

What is the smallest integer n for which 16n

Multiple choice — select the best answer

A2
B12
C4
D6

✓ Correct answer: D. 6 First convert 16n to the same base 4. You know 16 = 4 x 4 = 42 , so you can write 16n = (16)n = (42)n = 42n. We know that given 16n = 412, so we can write 42n = 412 Since both have ase 4, their powers are equal 2n = 12, or n = 6. Key takeaway: When solving problems involving exponents, base is to be seen carefully. It is easy to simplify, as long as they have the same base. Remember following simple formulae:am x an = am+n, am / an = a m-n , (am ) n = a m x n , (am ) 1/n = a m/ n

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