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If 3loga +5loga=log64.what is a?

User DisibioAaron
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1 Answer

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To solve this problem, we first need to use the properties of logarithms to combine the two logarithmic expressions on the left-hand side of the equation. Specifically, we can use the property that says loga(x) + loga(y) = loga(xy) to combine the two logarithms into a single logarithm: 3loga(a) + 5loga(a) = loga(a^3) + loga(a^5) = loga((a^3)(a^5)) = loga(a^8).

Next, we can use the property that says loga(b) = c if and only if a^c = b to solve for a. Since we are given that 3loga(a) + 5loga(a) = log64, we can set a^8 = 64 and solve for a: a^8 = 64, so a = 2^(1/8). Therefore, the value of a is approximately 1.19.
User Kashive
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