SOLUTION: help me pleasee!! Solve simultaneously: {{{log xy =7}}} , {{{log (x/y)= 10}}} so far ... if {{{log (base 10) (x/y)=10}}} this implies that {{{(x/y)=10}}} therfore, {{{x=10y}

Algebra.Com
Question 97794This question is from textbook Introducing Pure Mathematics
: help me pleasee!! Solve simultaneously:
,
so far ... if this implies that
therfore, ... thats all i got!
This question is from textbook Introducing Pure Mathematics

Found 3 solutions by jim_thompson5910, vincy_fyah, stanbon:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
, Start with the given system


, Rewrite the logs using the property <==>


, Rewrite as 10,000,000 for the first equation. Rewrite as 10 for the second equation


Solve the second equation for x by multiplying both sides by y

Plug in into the first equation. This will eliminate x so we can solve for y


Multiply


Divide both sides by 10


Divide


Take the square root of both sides. So this is our first answer



Plug in into to find x


Multiply


So our answer is
and


---------------------------------------------------------------------------

Check:

Start with the first equation


Plug in and


Multiply


Evaluate the left side. So the solutions and make the first equation true

---------------------------------------------

Start with the second equation


Plug in and


Divide

Evaluate the left side. So the solutions and make the second equation true

Answer by vincy_fyah(4)   (Show Source): You can put this solution on YOUR website!
.. sorry there...
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
log xy =7 , log (x/y)= 10
-----------
logx + logy = 7
logx - logy = 10
-------------
Add the two equations to get:
2logx = 17
log x = 8.5
x = 10^8.5
-----------
Substitute that into one of the equations with y and solve for y:
log(10^8.5) + log y = 7
8.5 + logy = 7
logy = 7-8.5
logy = -1.5
y = 10^(-1.5)
===================
Cheers,
Stan H.

RELATED QUESTIONS

Please help me solve this equation if log(x^3+3)base 10 - log(x+7)base 10 + log2base10=... (answered by MathLover1,MathTherapy,ikleyn)
Simultaneous equations log base 4 xy = 10 2 log base 8 x = 3 log base 8 y (answered by Theo)
Please help me solve this equation: log^7 100-log^7(y-5)=log^7... (answered by lwsshak3)
i need help with this... Solve simultaneously: {{{2log y = log 2 + log x}}} ,... (answered by stanbon)
if log base 10 y=0.7 + 2*log base 10 x , express y in terms of... (answered by hovuquocan1997)
Please help me solve this equation: if log x + log y =2, find... (answered by lwsshak3)
please help me solve this equation: if log x + log y = 2, find... (answered by lwsshak3)
solve for x log(base 10)X+log(base 10)(X+1) = log(base... (answered by nerdybill)
solve for x. log (base 10)(x+3)=log(base 10) (2x) + log (base 10)... (answered by lwsshak3)