Question

Find all solutions for x:
log2x+log2(x-6)=4

Answer 1

Okay, we first have to merge our log expressions together:
\[\log _{2} x+\log _{2}(x-6)=4\]\[\log _{2} x(x-6)=4\]\[\log _{2}\left( x ^{2}-6x \right)=4\]Now, can you take it from here? @kat50036

Answer 2

where did the 2nd \[\log_{2} \] go

Answer 3

Remember the log property we spoke of earlier. If two log expressions are added, then their interiors can be multiplied under a single log. The second log expression was simply merged with the first.

Answer 4

\[\log_{2} x ^{2}-6\log_{x} =4\]

Answer 5

Thats not right is it

Answer 6

^_^ that's an entirely different equation.

Answer 7

ugg

Answer 8

Thanks for your help Cardinal_Carlos

Answer 9

That's okay. We can start from where we left off:
\[\log _{2}(x ^{2}−6x)=4\]
From here, we simply use the logarithmic property and get:
\[x ^{2} - 6x = 2^{4}\]which simplifies to:
\[x ^{2} - 6x - 16 = 0\]
Now, we just factor out from here:
\[\left( x - 8 \right)\left( x + 2 \right) = 0\]
Our solutions are:\[x = -2 ~~~and ~~~x = 8\]

Answer 10

You're very welcome @kat50036 ^_^