CA FoundationIndices - equal powers with different bases
If 3^a = 5^b = 75^c, what is the value of ab - c(2a + b)?
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Answer: (b) 0 Let 3^a = 5^b = 75^c = k. 1. Then 3 = k^(1/a), 5 = k^(1/b), 75 = k^(1/c). 2. Since 75 = 3 x 5 x 5, we get k^(1/c) = k^(1/a) x k^(2/b). 3. Equate the powers: 1/c = 1/a + 2/b = (b + 2a)/ab. 4. So ab = c(2a + b), which gives ab - c(2a + b) = 0. Tip: Q33, Q35 and Q36 use the same trick. Put everything equal to k and break the last base into prime factors.
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1 answer 15 Nov 2026