If 27x = 9y. Find the value of \(\frac{x}{y}\)

Assessment: WAEC SSCE - General Mathematics - 2011 (Objective) Subject: General Mathematics

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If 27x = 9y. Find the value of \(\frac{x}{y}\)
Answer Details
If we can find the value of x and y, then we can calculate x/y by dividing x by y. Given: 27x = 9y We can rewrite 27 as 33 and 9 as 32 to get: (33)x = (32)y Applying the power of a power rule, we get: 33x = 32y For two exponential expressions to be equal, their bases must be equal. Therefore: 33x = 32y implies 3x = 2y Dividing both sides by y, we get: \(\frac{x}{y} = \frac{2}{3}\) Therefore, the answer is \(\frac{2}{3}\).
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