5*log6 x-4=2

Question

5*log6 x-4=2

saifoo.khan · Answer

$$\Large  5 \log_6 x-4 = 2$$that?

anonymous · Answer

@phi - so true!  I would really like to know what regular folks do with this stuff in real life.  It all seems so unnecessary!
Anyway I need help!

phi · Answer

the x-4 is part of the log?

anonymous · Answer

there is a multplication sign between the 5 and the log

saifoo.khan · Answer

same thing jenny.

anonymous · Answer

no the x-4 is ageer the log6 is stated, seperated by a space

saifoo.khan · Answer

same thing.

phi · Answer

solve for log x

anonymous · Answer

5*log6 x-4=2 ===> x-4 = 10^0.4 ===> x= 6.5119

anonymous · Answer

log6=x-4^5/2

phi · Answer

the 6 is the base, isn't it?

anonymous · Answer

that's the number at the bottom of the log, so yes?

phi · Answer

so you are solving for 
$$\log_6{x}$$
it's one thing

anonymous · Answer

what about the x-4?  Where does that come into it all?

saifoo.khan · Answer

i think it's obvious that it's (x-4)

phi · Answer

there isn't an x-4
it is log(x)-4  (where the log is base 6)

saifoo.khan · Answer

yes, it can be that way too^

anonymous · Answer

no it's simply states

5* log6  x - 4 = 2

phi · Answer

There is the idea of "order of operations"
parentheses, exponents (and logs and roots), mult/divide, add/subtract

phi · Answer

so the log takes precedence.  think of it as (log x) -4

anonymous · Answer

that makes no sense to me.  It says log6

phi · Answer

Doesn't it say
$$5 \log_6 x-4 = 2$$
the 6 is subscript, isn't it?

anonymous · Answer

yes, when I post questions, it doesn't allow me to do subscripts or exponents or anything like you post...sorry for the confusion

phi · Answer

So the x is attached to the log (base 6)  and the 4 isn't part of the log.
If we had written log(x-4) then the x-4 is part of the log

phi · Answer

You can't pry that x out of the log by any easy (add subtract, multiply, divide)  operation.
You solve for log(x)= stuff
and then you use the trick base^(log(x)) = base^stuff
which turns into x = base^stuff

anonymous · Answer

Ok so I am totally lost and I am going to give up on this one for the moment - on brain overload - THANKS!

phi · Answer

take a break, it might clear up later

anonymous · Answer

log 6^-.6 right?

phi · Answer

But here's the answer
$ 5 \log_6 x-4 = 2 $
$ 5 \log_6 x = 6 $      (add 4 to both sides)
$    \log_6 x = \frac{6}{5} $        (divide both sides by 5)
$  6^{\log_6 x}= 6^{\frac{6}{5}} $      ( 6 to the power of each side)
$   x  = 6^{\frac{6}{5}} $             (simplify the left hand side)

anonymous · Answer

Thanks!  I think I need a break - i am really on overload.
THanks you have been an awesome help!