Question

Solve for x. In(3x+2)=4

Answer 1

`\large\boxed{x=(e^4-2)/(3)}`

Explanation:

`\ln(3x+2)=4\\\\Domain:\ 3x+2>0\qquad\text{subtract 2 from both sides}\\\\3x>-2\qquad\text{divide both sides by 3}\\\\x>-(2)/(3)\\\\\ln(3x+2)=4\qquad\text{use the de}\text{finition of a logarithm:}\ \log_ab=c\iff a^c=b\\\\\ln(3x+2)=4\to\log_e(3x+2)=4\iff3x+2=e^4\qquad\text{subtract 2 from both sides}\\\\3x=e^4-2\qquad\text{divide both sides by 3}\\\\x=(e^4-2)/(3)\in D`