How do you find the derivative of $log_10 x$ ?

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Answer 1 · 2018-04-23T22:17:04

See below

Maybe learn how to base shift

Let $y = log_a b color(blue)( implies a^y = b)$

And for new base $Q$ :

$log_Q a^y= log_Q b implies y log_Q a= log_Q b$

So:

$y = color(red)( (log_Q b)/(log_Q a) = log_a b)$ <-- base-shifting

Pattern matching:

$d/(dx) (log_(10) x)$

$= d/(dx)( (log_e x)/(log_e 10) ) = d/(dx)( (ln x)/(ln 10) )$

$= (1)/(x ln 10)$

PS: Assumes you know that $(ln x)' = 1/x$

How do you find the derivative of log_10 xlog_10 x?