Question

If 27^x =64^y =125^z=60,find the value of 2013xyz/xy+yz+xz

Answer 1

670.25

Step-by-step explanation:

We have, $27^{x} = 64^{y} = 125^{z} = 60$ and we have to find the value of $\frac{2013xyz}{xy + yz + zx}$.

Now, $27^{x} = 60$.

Taking log on both sides we get,

x log 27 = log 60

⇒ $x = \frac{\log 60}{\log 27} = 1.24$ (Approx.)

Similarly, $y = \frac{\log 60}{\log 64} = 0.98$ (Approx.) and $z = \frac{\log 60}{\log 125} = 0.85$ (Approx.)

So, $\frac{2013xyz}{xy + yz + zx}$

= $\frac{2013 \times 1.24 \times 0.98 \times 0.85}{1.24 \times 0.98 + 0.98 \times 0.85 + 0.85 \times 1.24}$

= $\frac{2079.27}{3.1}$

= 670.25 (Answer)