2log3x-log3(x+4)=2

Question

2log3x−log3(x+4)=2
If the answer is not an integer, enter it as a decimal. Round to the nearest hundredth, if needed. If there are multiple solutions, separate the answers with semicolons (;).

Answer 1

2log₃x - log₃(x+4) = 2

 

log₃(x²) - log₃(x+4) = 2

 

log₃[x²/(x+4)] = 2

 

x²/(x+4) = 3²

 

x²= 9x+36

 

x²-9x-36 = 0

 

(x - 12)(x + 3) = 0

 

x = 12 or x = -3

 

-3 must be rejected because we can't take logs of negative numbers, so the only solution is 12.