What is x if ${log}_{2} (x) + {log}_{3} (x + 1) = {log}_{5} (x - 4)$ $log_2(x) + log_3(x + 1) = log_5(x - 4)$ ?

Question

2464 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-26T01:32:17

I do not think they are equal....

I tried various manipuations but I got an even more difficult situation!
I ended up trying a graphical approach considering the functions:

$f (x) = {log}_{2} (x) + {log}_{3} (x + 1)$ $f(x)=log_2(x)+log_3(x+1)$
and:
$g (x) = {log}_{5} (x - 4)$ $g(x)=log_5(x−4)$

and plotting them to see if they cross each other:

enter image source here

but they do not for any $x$ $x$ !

What is x if log2(x)+log3(x+1)=log5(x−4)log_2(x) + log_3(x + 1) = log_5(x - 4)?