Question

100 points! Please answer ASAP! Test tomorrow! Thankyou so much!!

Answer 1

here is the answer in pic

x= 1/2 and y= 1/3

Answer 2

(2x)^ln2 = (3x)^ln3 and 3^lnx =2^lny

solution :-

(2x)^ln2 = (3y)^ln3

take ln both sides

ln {(2x)^ln2 } = ln{(3y)^ln3 }

ln2× ln(2x) = ln3 × ln(3y)

ln2 × (ln2 + lnx ) = ln3 × ( ln3 + lny) -----(1)

now ,
3^lnx = 2^lny

take ln both sides

ln3 × lnx = ln2 × lny

lny = ln3× lnx /ln2

put equation (1)

ln2 ×(ln2 + lnx ) = ln3 × (ln3 + ln3 × lnx /ln2)

(ln2 )² + ln2 × lnx = (ln3)×ln2 + ln3 × lnx

(ln2)² -(ln3)× ln2 = (ln3 -ln2) × lnx

ln2(ln2 -ln3) =(ln3 -ln2)lnx

-ln2 =lnx

ln(1/2) = lnx

x = 1/2

hence , option ( C ) is correct