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}
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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.
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