Find the value of z in each of the following
a)3^(z+2)=81
b)2^-z = 128^-1

9514 1404 393

  a) z = 2

  b) z = 7

Step-by-step explanation:

a) 3^(z +2) = 81 = 3^4

  z +2 = 4 . . . . . . . . . . . equating exponents of the same base

  z = 2 . . . . . . . . . subtract 2

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b) 2^-z = 128^-1 = (2^7)^-1 = 2^-7

  -z = -7 . . . . . . . equating exponents of the same base

  z = 7 . . . . . . multiply by -1

Additional comment

It is helpful to know the small powers of small numbers like 2 and 3. Squares of numbers to 20 and cubes of numbers to 10 can also be useful to remember.

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