Multiple choice

Given that $10^{0.48} = x, 10^{0.70} = y$ and $x^{z} = y^{2}$, then the value of $z$ is (approximately) _________.

  1. $1.45$
  2. $1.88$
  3. $2.9$
  4. $3.7$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given 10^0.48 = x and 10^0.70 = y. x^z = y^2 implies (10^0.48)^z = (10^0.70)^2. Thus 0.48z = 1.40. z = 1.40 / 0.48 = 140/48 = 35/12 = 2.9166...

AI explanation

Substitute the given values into the equation x raised to the power of z equals y squared to get 10 raised to the power of 0.48z equals 10 raised to the power of 1.40. Because the bases are identical, the exponents must be equal, giving 0.48z equals 1.40. Solving this linear equation gives z equals 1.40 divided by 0.48. Dividing 140 by 48 gives z a value of approximately 2.9.

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