SOLUTION: {{{system((1/2)^(x+y)=16, log(x-y,8)=-3)}}}. Calculate the values of x and y

Algebra.Com
Question 173597: . Calculate the values of x and y
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
. Calculate the values of x and y

Let's simplify the equations.

Simplifying the first equation:



Write  as 
And write  as 



Remove the parentheses by multiplying the
inner exponent  by the outer
exponent , getting 



The base on each side is the same
positive number, which is not 1, so
we may equate the exponents:



Let's multiply every term by 



------

Now we simplify the second equation:



Use the rule of logs:   can be rewritten 



Write  as 



Enclose both sides in parentheses and raise to the
 power:



Multiply inner exponents by outer exponents:

 

Write the left side as  and right side as just  



Multiply both sides by 





Put the right side on the left and vice-versa:



------

So we now have this simpler system of equations:



I assume you know how to solve that system.
If you don't, post again asking how:

Answer:  

Edwin

RELATED QUESTIONS

{{{system((1/2)^(x+y)=16, log(x-y,8)=-3)}}} Calculate the values of x and... (answered by Edwin McCravy)
For each of the following equations either prove that it is correct (by using the rules... (answered by venugopalramana)
log x^2=y+3 log x=y-1 solve the... (answered by Fombitz)
Solve the system: log x^2=y+3 log x=y-1 (answered by josgarithmetic)
Use the properties of exponential and logarithmic functions to solve each system.... (answered by Edwin McCravy)
Given {{{2^x=8^(y+1)}}} and {{{9^y=3^(x-9)}}}, find the values of... (answered by Tatiana_Stebko)
Please help me solve the following system for (x,y): {{{log(9,x)}}} + {{{log(y,8)}}} = 2 (answered by Edwin McCravy)
Solve the following system for (x,y): {{{log(9,X)+ log(Y,8)=2}}} {{{log(X,9)+... (answered by sdmmadam@yahoo.com)
Show that {{{(log(9,(x/y)))=((1/2)(log(3,x)-log(3,y)))}}}. Hence, find the values of... (answered by Alan3354)