3^(x) = 4 4^{y} = 12 estimate xy ​

Question

`3^(x) = 4`
4^{y} = 12
estimate xy
​

Answer 1

9514 1404 393

Answer:

xy ≈ 2.3

Explanation:

Logarithms can be used to find x and y.

3^x = 4

x·log(3) = log(4)

x = log(4)/log(3)

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4^y = 12

y = log(12)/log(4)

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Then xy is ...

xy = log(4)/log(3) × log(12)/log(4) = log(12)/log(3)

xy ≈ 1.079/0.477

xy ≈ 2.26