How to solve this simultaneous equations which involves exponents: { <mtable columna

Jamiya Weber

Jamiya Weber

Answered question

2022-06-13

How to solve this simultaneous equations which involves exponents:
{ 2 x 2 y = 1 4 x 4 y = 5 3
Simultaneously. From the second equation I factorized to get
( 2 x + 2 y ) ( 2 x 2 y ) = 5 3
and from the first equation, since ( 2 x 2 y ) = 1, I deduced that
( 2 x + 2 y ) 1 = 5 3 ( 2 x + 2 y ) = 5 3
Now I am stuck on how to proceed.

Answer & Explanation

EreneDreaceaw

EreneDreaceaw

Beginner2022-06-14Added 20 answers

Try adding the equations 2 x 2 y = 1 and 2 x + 2 y = 5 3
To go further per your comment:
This gives 2 2 x = 8 3
Subtracting the equations gives 2 2 y = 2 3
Now recall that 2 a 2 b = 2 a b and divide in an appropriate way to make further progress.
veirarer

veirarer

Beginner2022-06-15Added 9 answers

{ 2 x 2 y = 1 2 x + 2 y = 5 3
so
2 x 2 y + 2 x 2 y = 2 2 x = 1 + 5 3 = 8 3 2 x = 4 3 x = l o g 2 4 3
Finally, since 2 x = 4 3 ,
2 y = 5 3 4 3 = 1 3 y = l o g 2 1 3
The solution is ( l o g 2 4 3 , l o g 2 1 3 )

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