Question

Solve the equation. Round to the nearest thousandth.

`- 5 + 2ln(3x) = 5`
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Answer 1

x= e^ 5 / 3 OR 49.471

Explanation:

-5=2In (3x)=5

determine the defined range

-5+2In (3x) = 5, x>0

move the constant to the right- move the five to the right and change the sign

2In (3x)= 5+5

calculate- add them together

2In (3x)=10

divide both sides by 2

In (3x)=5

covert into exponential form ( x=e^5)

3x= e^5

divide both sides by 3

x=e^5/3 , x> 0

(check if the solution is in the defined range) which is the answer

Answer 2

`x \approx \: \boxed{49.471}`

Explanation:

`- 5 + 2In(3x) = 5 \\ 2In(3x) = 5 + 5 \\ 2In(3x) = 10 \\ In(3x) = (10)/(2) \\ In(3x) = 5 \\ \implies \: 3x = {e}^(5) \\ \implies \: x = \frac{ {e}^(5) }{3} \\ x = (148.41316)/(3) \\ x = 49.4710533 \\ x \approx \: \boxed{49.471}`