Log_4*log_3*log_2(x^2-2x)=0 X=?

1 Answer
Jun 27, 2018

x=0, x=2

Explanation:

Factor log first as shown below:

log(4).log(3).log2(x^2-2x)=0

Take x^2-2x = x(x-2)

So now we get:

log(4).log(3).log(2).x(x-2)=0

Simplify log4 = log2^2 = 2log2

Remember log rule: log_a(x)^b = blog_x(x)

So now we get:

2log(2).log(3).log(2).x(x-2)=0

Apply exponential rule:

a^b.a^c = a^(b+c)

log(2) .log(2) = log2^(1+1) = log2^2

And we get:

2log(2).log(2)^2.log(3)x(x-2)=0

Using the zero factor principle, x=0

Solve x-2=0
we get x=2

So value of x=0, x=2

Hope this helps!