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

1 Answer
Tony B
Dec 19, 2016

#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#

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