Question about Functions

Question

The function f(x) = ln(2x + 2) has a root value of x = - 1/2.

How do you find the root value for this.

I would think..... 2x=-2 x=-1???

Answer 1

What is a root of an expression?

It is such a value of the argument ("x") that makes the expression equal to zero.

"ln" is a notation for a natural logarithm, the logarithm with the base "e" ("e" ≅ 2.71828).

Instead of writing log_e(....), we simply write ln(.....).

To find the root of this expression, we equal this expression to zero:

ln(2x + 2) = 0

Rewriting in the exponential form:

2x + 2 = e⁰

As you may recall, any number, raised to the 0-th degree, is equal to "1".

2x + 2 = 1

2x = - 2 +1

2x = -1

x = -1/2

Answer 2

ln(1) = 0

ln(2x+2) = 0 only when 2x+2 = 1 or 2x=--1 and x = 1/2

at (1,0) the graph of lnx crosses the x axis

and the graph of ln(2x+2) crosses the x axis when x=-2

Answer 3

ln(1) = 0

ln(2x+2) = 0 only when 2x+2 = 1 or 2x=--1 and x = 1/2

at (1,0) the graph of lnx crosses the x axis

and the graph of ln(2x+2) crosses the x axis when x=-2