WAEC SSCE - General Mathematics - 2011 (Objective)

Question 1 Report

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

\(\frac{1}{3}\)

\(\frac{2}{3}\)

1\(\frac{1}{2}\)

Answer Details

If we can find the value of x and y, then we can calculate x/y by dividing x by y. Given: 27^x = 9^y 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: 3^3x = 3^2y For two exponential expressions to be equal, their bases must be equal. Therefore: 3^3x = 3^2y 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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