Question

How do I solve ln(3x-5)=ln11+ln12

Answer 1

`\large\boxed{x=(137)/(3)}`

Explanation:

`\text{Use:}\\\\\ln a+\ln b=\ln(ab)\\\\\ln a=\ln b\Rightarrow a=b\\-------------\\Domain:\\\\3x-5>0\qquad\text{add 5 to both sides}\\\\3x>5\qquad\text{divide both sides by 3}\\\\x>(5)/(3)\\-----------------\\\\\ln(3x-5)=\\11+\ln12\\\\\ln(3x-5)=\ln(11\cdot12)\\\\\ln(3x-5)=132\iff3x-5=132\qquad\text{add 5 to both sides}\\\\3x=137\qquad\text{divide both sides by 3}\\\\x=(137)/(3)`