Question

How do you solve `ln(5.6-x)=ln(18.4-2.6x)`?

Answer 1

`x=8`

Explanation:

An example of line of thought.

Suppose we had: `10xx2=10xx(1+1)`

Because both sides are multiplied by 10 we can and may remove the `color(brown)(ul(" operation of "))` multiplying by 10 and the equation will still be true.

`color(brown)("Taking loges on both sides is an operation")`

Given that `" "ln(5.6-x)=ln(18.4-2.6x)" "` is true

Then also `" "color(white)(..)5.6-xcolor(white)(.)=color(white)(....)18.4-2.6x" "` is equally true
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write as:`color(white)(.)2.6x-x=18.4-5.6`

`1.6x=12.8`

`x=12.8/1.6 =128/16 =8`