Question

The number of ordered pairs (x, y) satisfying $3^x.5^y=75$ and $3^y.5^x=45$ is

• A. 0
• B. 1
• C. 3
• D. none of these

Answer 1

Answer: (B)

The equation are $3^x\cdot 5^y=75\dots (1)$
and $3^y\cdot 5^x=\mathrm{45.....}$(2)
Dividing the two equations, we get
${\left(\frac{3}{5}\right)}^{x-y}=\frac{75}{45}=\frac{5}{3}$
$\Rightarrow x-y=-\mathrm{1.....}$(3)
Multiplying equations (1) and (2), we get
$(15{)}^{x+y}=45\times 75=(15{)}^3$
$\Rightarrow x+y=\mathrm{3......}$(4)
solving $(3)$ and $(4)$ we get $x=1,y=2$