MATH 041 Lecture 12: 3.2 LOGARITHMIC FUNCIONS AND THEIR GRAPHS

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For x > 0, a > 0 and a 1 y = logax x = ay read log base a of x . Q: how many of one number (a) do we need to get another number (x)? f(x) = logax log28 = 3 8 = 23. 2 special bases of logs log10x log10 = 1 log100 = 2 log0. 1 = -1 base is assumed to be 10. 10-1 = 1/101 ln(x) logex = ln(x) natural log base e . Graph f(x) = log(x) base 10 x f(x) 2 log5125 = 3 log31/9 = -2 log232 = 5 log41/64 = -3. 4) loga1 = 0 logaa = 1 logaax = x if logax = logay, then x = y log2(x+3) = log27 x+3 = 7 x = 4. Change of base property logax = (logbx)/(logba) log330 = (ln30)/(ln3) log330 = (log30)/(log3) Product property: loga(uv) = logau + logav. Quotient property: loga(u/v) = logau - logav.

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