Base or Log ?

Calculus Level 1

Evaluate d d x log ⁡ 10 x \frac{{d}}{{d}x}\log_{10} {x} at x = 3 x = 3 .


The answer is 0.1447648273011.

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Rajdeep Dhingra by Rajdeep Dhingra , 20, India

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2 solutions

Tanishq Varshney
Mar 13, 2015

2.303 l o g 10 x = l o g e x 2.303log_{10} x=log_{e} x

1 2.303 d d x l n x \frac{1}{2.303}\frac{d}{dx}lnx

= 1 2.303 x \frac{1}{2.303x}

at x = 3 x=3

1 6.909 \frac{1}{6.909} = 0.1447 \boxed{0.1447}

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Noel Lo
May 13, 2015

Convert l o g 10 x = l n x l n 10 log_{10} x = \frac{ln x}{ln 10} first.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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