How do you solve ln(x-6) - ln(5) = ln(7) + ln(x-2)ln(x6)ln(5)=ln(7)+ln(x2)?

1 Answer
Jul 10, 2016

x=65/34x=6534

Explanation:

Subtraction of logs is the consequence of the source values being divided. So ln(x-6)-ln(5) ->ln((x-5)/5)ln(x6)ln(5)ln(x55)

Addition of logs is the consequence of the source values being multiplied. So ln(7)+ln(x-2)->ln(7(x-2))ln(7)+ln(x2)ln(7(x2))

Putting this all together

ln((x-5)/5)=ln(7(x-2))ln(x55)=ln(7(x2))

=>(x-5)/5=7(x-2)x55=7(x2)

x-5=35(x-2)x5=35(x2)

x-5=35x-70x5=35x70

34x=6534x=65

x=65/34x=6534