Question 137

If $$8^x 2^y = 512 and 3^{3 x + 2 y} = (3^2)^{(3 * 2)}$$ then what is the value of $$x$$ and $$y$$ ?

Solution

Given : $$8^x 2^y = 512$$

=> $$2^{3x}\times 2^y = (2)^9$$

=> $$2^{3x+y}= (2)^9$$

=> $$3x+y=9$$ -----------------(i)

Also, $$3^{3 x + 2 y} = (3^2)^{(3 * 2)}$$

=> $$3^{3x+2y}= (3)^{12}$$

=> $$3x+2y=12$$ -----------------(i)

Solving equations (i) and (ii), we get : $$x=2$$ and $$y=3$$

=> Ans - (B)

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