Question 11

What are the values of x and y that satisfy both the equations?

$$2^{0.7x} * 3^{-1.25y} = 8\sqrt{6}/27$$

$$4^{0.3x} * 9^{0.2y} = 8*81^{1/5}$$

Solution

$$2^{0.7x} * 3^{-1.25y} = 8\sqrt{6}/27$$ => $$2^{0.7x} * 3^{-1.25y}$$ = $$2^{3.5} * 3^{-2.5}$$

=> 0.7x = 3.5 => x = 5

=> -1.25y = -2.5 => y = 2

$$4^{0.3x} * 9^{0.2y} = 8*81^{1/5}$$ => $$2^{0.6x} * 3^{0.4y}$$ = $$2^3 * 3^{0.8}$$

=> 0.6x = 3 => x = 5

=> 0.4y = 0.8 => y = 2

=> (5,2) is the solution.

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