How do you solve $ln (3 x + 1) - ln (5 + x) = ln 2$ $ln(3x+1)-ln(5+x)=ln2$ ?

Question

7840 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-01T08:48:02

$x = 9$ $x=9$

$ln (3 x + 1) - ln (5 + x) = ln (2) \Rightarrow$ $ln(3x+1)-ln(5+x)=ln(2)=>$ using laws of logs:

$ln [\frac{3 x + 1}{x + 5}] = ln (2) \Rightarrow$ $ln[(3x+1)/(x+5)]=ln(2)=>$ if $ln (A) = ln (B) \Leftrightarrow A = B$ $ln(A)=ln(B)hArrA=B$ :

$\frac{3 x + 1}{x + 5} = 2 \Rightarrow$ $(3x+1)/(x+5)=2=>$ multiply by $(x + 5)$ $(x+5)$ :

$3 x + 1 = 2 (x + 5) \Rightarrow$ $3x+1=2(x+5)=>$ expand right side:

$3 x + 1 = 2 x + 10 \Rightarrow$ $3x+1=2x+10=>$ subtract $- 2 x$ $-2x$ and 1 from both sides:

$3 x - 2 x = 10 - 1 \Rightarrow$ $3x-2x=10-1=>$ simplify:

$x = 9$ $x=9$

How do you solve ln(3x+1)−ln(5+x)=ln2ln(3x+1)-ln(5+x)=ln2?