SOLUTION: Can someone help me solve this?: {{{ log( 5, x ) + log ( 5, 125 ) /log ( 5, x ) = 7/2 }}}

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Question 1121541: Can someone help me solve this?:
+log%28+5%2C+x+%29+%2B+log+%28+5%2C+125+%29+%2Flog+%28+5%2C+x+%29+=+7%2F2+
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2Cx%29%2B3%2Flog%285%2Cx%29=7%2F2

Let v=log%285%2Cx%29
Use that to make the substitution for log%285%2Cx%29,
and you can write
v%2B3%2Fv=7%2F2 .
There is no "moving v underneath". There is not yet any "v%5E2".

Solve this for v.


Next steps may be, multiply left and right sides by lowest or simplest common denominator of 2v. (Basic fractionss skills).
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2v%28v%2B3%2Fv%29=2v%287%2F2%29
2v%5E2%2B6=7v
2v%5E2-7v%2B6=0----------maybe you can continue on your own from this.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
log 5 x=z
z+(3/z)=7/2
z^2-3.5z+3=0
2z^2-7z+6=0
(2z-3)(z-2)=0
z=3/2 and z=2
log 5 x=2
x=25 That checks in that 2+3/2=7/2
log 5 x=1.5
x=11.18 that checks in that 1.5+3/1.5=7/2