Equivalence of Logarithmic Expressions: Solving a Simple Algebra Question

[whatlifeforme]

Homework Statement

how are these two problems equivalent?

Homework Equations

9 * ln | sqrt(4+x^2)/2 + x/2 | --->> = 9 * ln | sqrt(4+x^2) + x|

The Attempt at a Solution

i assume this has something to do with log rules.

 

[Dick]

Homework Statement

how are these two problems equivalent?

Homework Equations

9 * ln | sqrt(4+x^2)/2 + x/2 | --->> = 9 * ln | sqrt(4+x^2) + x|

The Attempt at a Solution

i assume this has something to do with log rules.

Those aren't problems, they are expressions. And they aren't equivalent, they are different numbers when you put a value in for x. What is true is that they have the same derivative. ln(f(x)/2)=ln(f(x))-ln(2). If you differentiate the derivative of ln(2) is zero.