What is x if $log_2(x) + log_3(x + 1) = log_5(x - 4)$ ?

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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:

$f(x)=log_2(x)+log_3(x+1)$
and:
$g(x)=log_5(x−4)$

and plotting them to see if they cross each other:

enter image source here

but they do not for any $x$ !

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)?