Hey guys , can you explain me why in log equation log5x = log2 + log2x +1, I can’t undo logs individually so it’s become 5x = 2 + 2x +1
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It’s because the logarithm function is not linear. This simply means that log(a + b) ≠ log(a) + log(b). Another function lacking the property of linearity is the much more commonly known square function, where it is such a commonly made assumption that squaring is linear to the point that teachers have to explicitly tell students that (a + b)^(2) ≠ a^(2) + b^(2).
An easy way to prove that logarithms aren’t linear is by simply testing two select values. For example, we could check a = b = 1. On the left side we have log(2), and on the right side we have log(1) + log(1), which is simply 0 (x^(0) = 1 for nonzero x). Obviously, log(2) is not equal to 0, so our assumption that the logarithm was linear was demonstrably incorrect.
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