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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ok so mathematicians are really bad at choosing words for things. you know how addiction and subtraction are inversions of each other? like, 3 + 4 = 7 and 7 – 4 = 3 are saying the same fact from different perspectives?
well, logarithms, exponents, and radicals (you probably know radicals as “roots” as in “square root”) are saying the same fact from three different perspectives. 2 to the 3rd power is 8. log base 2 of 8 is 3. the 3rd root of 8 is 2. these are all the same fact, just written different ways.
the easiest way i’ve learned to remember it is to just revert to exponents. log base X of Y = Z is asking the question “what power Z do i have to choose so that X ^ Z = Y?”
one other note: you’ll often run into logarithms that don’t specify a base. this could be one of two things, and hopefully your teacher or the authors of your textbook will tell you which one they’re using. it could mean that the base is 10: especially in cases where you’re using scientific notation, log base 10 can be really useful. however it could also mean a very special and complicated number called e. e is around 2.718. e is basically the number which makes logarithms and exponents play well with calculus, but it has a bunch of other funky properties too.
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