Given that 10^0.48 = x, 10^0.70 = y and x^z = y^2, then the value of z is closest to _____?
- 2.9
- 1.45
- 1.88
- None of these
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.
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