## recon14193 2 years ago solve a log

1. recon14193

\[\log_{a}x+\log_{a}x-2=\log_{a}x+4 \]\ \[\log_{a}x(x-2)=\log_{a}x+4\] that is my work so far I do not know how to convert to exponential

2. recon14193

I am wondering if I divide by \[\log_{a}x+4\] and then have it equal to zero which means my final answer is just 1

3. satellite73

assuming the right hand side is \(\log_a(x+4)\) then your last job is to solve \[x(x-2)=x+4\]

4. recon14193

so the logs just drop out

5. satellite73

log is a "one to one function" so if \[\log(A)=\log(B)\] then \(A=B\)

6. recon14193

ok I guess but I dont really understand

7. satellite73

8. satellite73

if you were told that \[2a+4=2b+4\] then you would know that \(a=b\) right?

9. satellite73

it is the same with the log if \(\log(x)=\log(y)\) then you know \(x=y\)

10. satellite73

in other words, as in your example, the only way for \(\log(x^2-2x)\) to be equal to \(\log(x+4)\) is if \(x^2-2x=x+4\)

11. recon14193

oh I see now so if i understand correctly it is because we know they must be equal that the fact that it is a log of each does not matter because no matter what they yield the same result

12. satellite73

yes, exactly

13. recon14193

Thank you I appreciate your help

14. satellite73

if i know \(\log(x)=\log(5)\) then i know that \(x=5\) i cannot be anything else

15. satellite73

yw