Question

log(x-1)+log(x+1)=log2 1

Answer 1

Answer:

There are no solutions.

Explanation:

Use the logarithm rules to simplify either side:

Left hand side: loga+logb=log(ab)Right hand side: bloga=log(ab)

This gives

log[(x−1)(x+1)]=log[(x+2)2]

This can be simplified using the following rule:

If loga=logb, then a=b

Giving us:

(x−1)(x+1)=(x+2)2

Distribute both of these.

x2−1=x2+4x+4

Solve. The x2 terms will cancel, so there will only be one solution.

4x=−5

x=−54

However, this solution is invalid. Imagine if xactually were −54. Plug it into the original equation. The terms log(x−1) and log(x+1)would be log(−94) and log(−14), and the logarithm function loga is only defined when a>0. I THINK THIS WILL HELP YOU ! THANK YOU ☺☺