Explanation

1. 10^0.48 = x

2. 10^0.70 = y

3. x^z = y^2

We can rewrite the third equation as:

(10^0.48)^z = (10^0.70)^2

Using the power rule of exponents:

10^0.48z = 10^1.40

Since the bases are the same (both are 10), we can equate the exponents:

0.48z = 1.40

Now, divide both sides by 0.48:

z ≈ 1.40 / 0.48

z ≈ 2.92

So, the value of z is closest to 2.9.