What is the tangent of y=log_{10}(x-1),\at x=2 ?

The tangent of y=log_{10}(x-1),\at x=2 is y= 1/(ln(10))x-2/(ln(10))

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tangent of y=log_{10}(x-1),\at x=2

tangent of

y = lo g_{10} (x - 1), at x = 2

y = \frac{1}{ln ( 10 )} x - \frac{2}{ln ( 10 )}

Solution steps

Find the tangent point:

(2, 0)

Find the slope of

y = lo g_{10} (x - 1) : \frac{d y}{d x} = \frac{1}{ln ( 10 ) ( x - 1 )}

Compute the slope of

y = lo g_{10} (x - 1)

x = 2 : m = \frac{1}{ln ( 10 )}

Find the line with slope m=

\frac{1}{ln ( 10 )}

and passing through

(2, 0) : y = \frac{1}{ln ( 10 )} x - \frac{2}{ln ( 10 )}

y = \frac{1}{ln ( 10 )} x - \frac{2}{ln ( 10 )}

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What is the tangent of y=log_{10}(x-1),\at x=2 ?
The tangent of y=log_{10}(x-1),\at x=2 is y= 1/(ln(10))x-2/(ln(10))