Question

If $2^x\cdot 2^y=3^z$, then $\frac{x+y}{z}$ is equal to:

• A. $1.330$
• B. $1.750$
• C. $0.750$
• D. $1.585$
• E. $1.425$

Answer 1

Answer: (D)

$1.585$

Given $2^x.2^y=3^z$
$\Rightarrow 2^x.2^y=2^{(x+y)}=3^z$
Now apply logarithm on both sides, we get $(x+y)\log 2=z\log 3$
Therefore $\frac{(x+y)}{z}=\frac{\log 3}{\log 2}=1.585$