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

Question

2728 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-10T09:01:41

#x=65/34#

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

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

Putting this all together

#ln((x-5)/5)=ln(7(x-2))#

#=>(x-5)/5=7(x-2)#

#x-5=35(x-2)#

#x-5=35x-70#

#34x=65#

#x=65/34#