How do you find the derivative of $f(x) = log_x (3)$ ?

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Answer 1 · 2016-06-01T20:15:10

$(df)/(dx)(x) = -log_e3/(x log_e^2(x))$

$y = log_x 3 = (log_b 3)/(log_b x)$ for any convenient basis $b$

Calling now $g(x,y) = y log_e x - log_e 3 = 0$ after taking $b = e$ , we have

$dg = g_x dx + g_y dy = 0$

then

$(dy)/(dx) = - (g_x)/(g_y) = -((y/x))/(log_e x) = -y/(x log_e(x)) = -log_e3/(x log_e^2(x))$

How do you find the derivative of f(x) = log_x (3)f(x) = log_x (3)?