Solve the logarithmic equation log x 3 logx log 18 algebr

Solve the logarithmic equation log (x - 3) + logx = log 18 algebrically.

Solution

log(x-3)+log x = log 18

As we know, log p + log q = log (p*q), applying same in above we get

log((x-3)*x) = log 18

Taking antilog on both sides

(x-3)(x)=18 => x²-3x=18 => x²-3x-18=0 => x²-6x+3x-18=0 => x(x-6) + 3(x-6)=0

=>(x+3)(x-6)=0 => x+3=0 or x-6=0 => x=-3 or 6