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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Simply put this is an algebra problem and algebra is hard. Calculus is easy. Algebra is where you will make the mistakes.
I’m assuming you know logarithms is the inverse of exponents. It’s now applying that fact to algebra.
What you do to one side, you do to the other.
log5x = log2 + log2x +1 => 10^(log5x) = 10^(log2 + log2x +1)
The “10^” in 10^(log2 + log2x +1) does not distribute. To “distribute” them, it needs to be 10^(log2)*10^(log2x)*10^(1). So 5x = 40x.
I usually just substitute in easy numbers to test things. It makes concepts stick better than listening to the teacher and misremembering/not remembering concepts.
10^(2+2+1) = 10000 <- original
10^2 + 10^2 + 10^1 = 100 + 100 + 10 = 210 =/= 10000 <- yours
10^2 * 10^2 * 10^1 = 100 * 100 * 10 = 10000 = 10000 <- correct
Why does it do this? I can only answer that’s how it is or that’s above my pay grade but using simple math I can show that what you did is wrong, which is enough to pass math class.
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