Solve for x Log base 3 (2x-5) - Log bas 3( x^2 + 4x+4)= 2

Answer 1

This equation is a logarithmic equation that uses some of the logarithmic properties.

If we have log₃(2x-5) - log₃(x²+4x+4) =2 .. here we will use the property for substraction :

log_a^m - log_aⁿ = log_a(m/n) .

therefore log₃(2x-5) - log₃(x²+4x+4) =l og₃(2x-5)/(x²+4x+4)

log₃(2x-5)/(x²+4x+4) = 2 ( we cannot solve a log equation if we don't have the same logs , therefore we want to convert 2 as log₃9 )

log₃(2x-5)/(x²+4x+4) = log₃9

since we have log of something = log of something we can remove the logs and assume that

(2x-5)/(x²+4x+4) = 9 ( now we solve from here . Please keep in mind the domain and your restrictions for this equation since you use log function )

your condition for the equations should be 2x-5 > 0 and x²+4x+4)

to solve this equation we cross multiply 2x-5 = 9(x²+4x+4)

2x-5 =9x²+36x+36 ( we distributed the 9 from right side )

9x²+34x+41 = 0 ( set the equation in the standard form by moving everything on one side )