Question

Solve for x. 2 - In(x + 3) = In 4 O x= In 4-1 O x = 2e x=2-3 X = -3

Answer 1

Starting with the equation:

`2-\ln (x+3)=\ln (4)`

Add ln(x+3) to both sides:

`2=\ln (4)+\ln (x+3)`

Use the property:

`\ln (a)+\ln (b)=\ln (a\cdot b)`

to rewrite the right hand side of the equation:

`2=\ln (4(x+3))`

Use the distributive property to rewrite 4(x+3) as 4x+12:

`2=\ln (4x+12)`

Use the property:

`a=b\Rightarrow c^a=c^b`

for a=2, b=(4x+12) and c=e:

`e^2=e^(\ln (4x+12))`

Use the property:

`e^(\ln (a))=a`

to rewrite the right hand side of the equation:

`e^2=4x+12`

Substract 12 from both sides of the equation:

`e^2-12=4x`

Divide both sides by 4:

`(e^2)/(4)-3=x`

Substitute the value of x into the original equation to check the answer.