How do you find the derivative of $log_(3)x$ ?

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Answer 1 · 2016-03-15T04:30:51

$frac{"d"}{"d"x}(log_3(x)) = 1/(xln(3))$ .

There is an identity that states

$log_a(b) = frac{ln(a)}{ln(b)}$ ,

for $a > 0$ and $b > 0$ .

So, we can write

$log_3(x) = ln(x)/ln(3)$

for $x > 0$ .

So to find the derivative, it helps if you know that

$frac{"d"}{"d"x}(ln(x)) = 1/x$ .

So,

$frac{"d"}{"d"x}(log_3(x)) = frac{"d"}{"d"x}(ln(x)/ln(3))$

$= 1/ln(3) frac{"d"}{"d"x}(ln(x))$

$= 1/(xln(3))$ .

How do you find the derivative of log_(3)xlog_(3)x?