Question

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the given point. See Example 5.

g(x) = log10 2x; (5, 1)

Answer 1

`x=5y`

Explanation:

We are given that

`g(x)=log_(10)(2x)`

Point(5,1)

`g(x)=(ln(2x))/(log10)`

By using property

`log_x y=(lny)/(lnx)`

We have to find the equation of tangent line to the given graph.

Differentiate w.r.t x

`g'(x)=(1)/(2xlog 10)* 2`

By using the formula

`(d(lnx))/(dx)=(1)/(x)`

`(dy)/(dx)=(1)/(xlog 10)`

We know that Log 10=1

`m=g'(x)=(1)/(x)`

Substitute x=5

`m=(1)/(5)`

Point-slope form

`y-y_1=m(x-x_1)`

By using this formula

`y-1=(1)/(5)(x-5)`

`5y-5=x-5`

`x-5y=-5+5=0`

`x=5y`

Hence, the equation of tangent line to the graph

`x=5y`