Question

Solve:
answer the question for z
z= ?

Answer 1

z=3/8

Explanation:

Step by step summary

We have to remember some of these basic indices’ corollary

1. (1/a)ⁿ = (a)⁻ⁿ
2. (a²)ⁿ = (a)²ⁿ
3. (a)ᵇ.(a)ⁿ = (a)ᵇ⁺ⁿ

Using these corollaries we would proceed with the problem

(1/4)^(3z-1)= (4)^(1-3z) using 1 theorem

Similarly

(16)^ (z+2)= (4)^(2(z+2)) using 2nd theorem

(64)^ (z-2)=(4)^ (3(z-2)) using 2nd theorem

Solving above 2 equations we get

(4)^(2z+4). (4)^(3z-6)

(4)^(2z+4+3z-6) using 3rd theorem

(4)^(5z-2)

Thus, we get the equation

(4)^(1-3z) = (4)^(5z-2)

Since the bases are the same we could equate the powers

1-3z=5z-2

8z=3

Z=3/8