Question

Given that $87^{0.27} = x$, $87^{0.15}= y$ and $x^z = y^6$ , then the value of z is close to:

• A. 5.77
• B. 2.15
• C. 3.16
• D. 3.33

Answer 1

Answer:

D. 3.33

Let's solve this problem using the properties of exponents:

1. Express x and y in terms of 87:

   • $x = 87^{0.27}$

   • $y = 87^{0.15}$

2. Substitute x and y into the equation x^z = y^6:

   • $(87^{0.27})^z = (87^{0.15})^6$

3. Apply the power of a power rule $(a^m)^n = a^{m*n}$:

   • $87^{0.27z} = 87^{0.15 * 6}$

   • $87^{0.27z} = 87^{0.9}$

4. Since the bases are the same, equate the exponents:

   • 0.27z = 0.9

5. Solve for z:

   • z = 0.9 / 0.27

   • z = 90 / 27

   • z = 10 / 3

   • z = 3.333...

Therefore, the value of z is close to 3.33.