Question

Solve the equation \[\log_{x} 5 + 3\log_{5} x +4 =0\]

Answer 1

I suppose we could let \(\large u = \log_x5\) for the time being...

Answer 2

not forgetting of course that
\[\Large \log_5x = \frac1{\log_x5}\]

Answer 3

So, it then becomes
\[\large u + \frac3u + 4=0\]

Answer 4

how do you go on from there? :/

Answer 5

@terenzreignz ?

Answer 6

multiply entire thing wid u, you will see a quadratic, solve it

Answer 7

Multiplying through with u...
\[\large u^2 + 3 + 4u = 0 \]

Solve for u. (This can be done most easily by factoring)