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

Dec 19, 2016

$x = 8$

#### Explanation:

An example of line of thought.

Suppose we had: $10 \times 2 = 10 \times \left(1 + 1\right)$

Because both sides are multiplied by 10 we can and may remove the $\textcolor{b r o w n}{\underline{\text{ operation of }}}$ multiplying by 10 and the equation will still be true.

$\textcolor{b r o w n}{\text{Taking loges on both sides is an operation}}$

Given that $\text{ "ln(5.6-x)=ln(18.4-2.6x)" }$ is true

Then also $\text{ "color(white)(..)5.6-xcolor(white)(.)=color(white)(....)18.4-2.6x" }$ is equally true
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Write as:$\textcolor{w h i t e}{.} 2.6 x - x = 18.4 - 5.6$

$1.6 x = 12.8$

$x = \frac{12.8}{1.6} = \frac{128}{16} = 8$