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lisabon 2012 [21]
3 years ago
12

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressio

ns. Give the exact answer. log x plus log (x minus 3 )equals log 54
Mathematics
1 answer:
KIM [24]3 years ago
8 0

Answer:

Therefore x=9

Step-by-step 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

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