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

Answer:

$x=5y$

Step-by-step explanation:

We are given that  

$g(x)=log_{10}(2x)$

Point(5,1)

$g(x)=\frac{ln(2x)}{log10}$

By using property

$log_x y=\frac{lny}{lnx}$

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

Differentiate w.r.t x

$g'(x)=\frac{1}{2xlog 10}\times 2$

By using the formula

$\frac{d(lnx)}{dx}=\frac{1}{x}$

$\frac{dy}{dx}=\frac{1}{xlog 10}$

We know that Log 10=1

$m=g'(x)=\frac{1}{x}$

Substitute x=5

$m=\frac{1}{5}$

Point-slope form

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

By using this formula

$y-1=\frac{1}{5}(x-5)$

$5y-5=x-5$

$x-5y=-5+5=0$

$x=5y$

Hence, the equation of tangent line to the graph

$x=5y$