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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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