solve the logarithmic equation

Question

1.) log₃(x-3)=1+log₃(x+1)

 

2.)lne^3x-27=log1

 

Answer 1

1.

log₃(x-3)=1 + log₃(x+1)

3^log₃(x-3) = 3^{(1 + log₃(x+1))}

x - 3 = 3¹ * 3 ^log₃(x+1)

x - 3 = 3 * (x + 1)

x - 3 = 3x + 3

-2x = 6

x = -3

 

2. 

ln e^3x-27= log 1

3x-27 = 0  (Because the log of 1 is always 0, no matter what base is used)

3x = 27

x = 9