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:

$\frac{e^2}{4}-3=x$

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