Question

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. log x plus log (x minus 3 )equals log 54

Answer 1

Therefore x=9

Explanation:

Give that,

log x+ log (x-3) = log 54

log x(x-3) =log 54 [
`log_ca+log_c b=log_c(ab)` ]

x(x-3) = 54

Now expand the above equation to get a quadratic equation

x²-3x=54

⇒x²-9x+6x-54=0

⇒x(x-9)+6(x-9)=0

⇒(x-9)(x+6)=0

⇒x-9=0 or, x+6=0

⇒x=9,-6

Now putting x= -6 in the given expression,

log(-6)+log(-6-9)=log 54.

Since log (-6) does not exist.

Therefore x=9