5^a = 1/25, 5^b = 25sqrt(5), 5^c = 1/sqrt(5). What is the value of a + b + c?
Two ways to do it. Manually work them all out: 5a = 1/25 means a = -2, 5b=25sqrt(5) means b = 2.5, 5c = 1/sqrt(5) means c = -0.5. So a + b + c = -2 + 2.5 + 0.5 = 0.
Can alternatively remember that (xt)(xu) = xt+u (when multiplying you add powers). This means that 5a5b5c = 5a+b+c = (1/25)(25sqrt(5))(1/sqrt(5)) = 1. We know that 50 = 1, so a + b + c = 0.
CH
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