Please help me solve this log equation

Question

Solve the equation

  log_3^x=1-log_3^(x+2)

Answer 1

I assume the equation is

 

log₃ x = 1 - log₃(x + 2)

 

 

Add log₃(x + 2) to get all logs on one side of equation.

 

log₃x + log₃(x + 2) = 1

 

 

We can rewrite this as a product of logs.

 

log₃[x(x + 2)] = 1

log₃(x² + 2x) = 1

 

The solution of a logarithm is the exponent. Our base of the exponent is 3.

 

3¹ = x² + 2x

 

3 = x² + 2x

 

0 = x² + 2x - 3

0 = (x + 3)(x - 1)

 

x = -3          and       x = 1

 

Accept      x = 1