Can someone explain how to do logx+log(x-3)=log(5x)? Find value of x

Use the rules of logs.

log(a) + log(b) = log(ab)

log(x) + log(x-3) = log(x*(x-3)) = log(5x)

So x*(x-3) = 5x. Solve that for x.

Hello,

Simplicity itself: you just have to remember two things:
▪ Logarithmic functions are only defined for positive values.
▪ Considering two positive reals a and b, log(a) + log(b) = log(ab)

Hence
log(x) + log(x - 3) = log (5x)
log[x(x - 3)] = log(5x)
x(x - 3) = 5x
x² - 3x - 5x = 0
x(x - 8) = 0
So either x=0 or x=8.

Since logarithmic functions are only defined for positive values, x=0 is unvalid and:
x = 8

Logically,
Dragon.Jade :-)