Asked by dam

5logxbase4+48log4basex=x/8
help me plz step
Answered by Reiny
5logxbase4+48log4basex=x/8
--->

5 log <sub>4</sub> x + 48log <sub>x</sub> 4 = x/8

One of rules of logs:
log <sub>a</sub> b = 1/log <sub>b</sub> a
and furthermore:
log <sub>a</sub> b = log b/log a
so
5 log <sub>4</sub> x + 48log <sub>x</sub> 4 = x/8

I don't know of any nice method to solve this, I ran it through Wolfram and got x = 2130.13 , which satisfies the original equation

http://www.wolframalpha.com/input/?i=solve+5(log4)%2Flogx+%2B+48logx%2Flog4+%3D+x%2F8
Answered by Reiny
My equation near the end should have included:

5 log 4 x + 48log x 4 = x/8
5 log<sub>4</sub> x + 48/log<sub>4</sub> x = x/2
or
5log 4/log x + 48log x/log 4 = x/2

btw, that is what I used in Wolfram , so my answer stands as is
Answered by Steve
If we let
u = log_4(x) then x = 4^u and we have

5u + 48/u = 4^u/8
the solution to this is u=4

so, x=4^u = 256
Answered by Mubaraq
Steve how did you get u=4?
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