Question

If w³ = x² = y⁸ = z¹⁰ then find value of log_y (wxz) + log_z (w)

1. 151/11
2. 162/15
3. 159/7
4. 158/4

Answer 1

Correct Answer - Option 2 : 162/15

Calculation:

w³ = y⁸

⇒ w = y^8/3

Similarly, w = z^10/3, x = y⁴, z = y^4/5

Now, log_y (wxz) + log_z (w)

⇒ log_y (y^8/3 × y⁴ × y^4/5) + log_z (z^10/3)

⇒ log_y (y^{(8/3) + 4 + (4/5)}) + (10/3)

⇒ (112/15) + (10/3)

⇒ 162/15

∴ required answer is 162/15

 X^y × X^a × X^b = X^{Y + a + b}