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Which of the following best approximates the value of q if \(5^{28}+3^{11}=5^q?\)

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Re: Which of the following best approximates the value of q if \(5^{28}+3^{11}=5^q?\)

by regor60 » Sun Apr 25, 2021 9:43 am
3^3 =27 and 5^2 = 25
Problem asks for approximate answer, so the above are approximately equal.
So using the above 3^9 = 5^6, so 3^11 is about equal to 9*5^6

5^28 + 9*5^6 = 5^q

Divide by 5^6

5^22 +9 = 5^(q-6)

In the context of these large numbers, 9 is effectively 0, so

5^22 =5^(q-6)
So q =28, C
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