Question

The reals x and y satisfy log2x + logą(y2) = 5 and loggy + logą(x2) = 7 then the value of xy is​

Answer 1

$\bigstar \: \boxed{\sf{\color{purple}{Answer:}}}$

$\huge\underline\mathtt\red{Hola}$

Taking log on both sides of given equations.

log 3 log (3x) = log 4 log (4y);

log3(log 3+log x)=log4(log 4+logy)

[ log(ab)=log a+log b] Rightarrow

(i) And, log x log 4 = log y log 3; log x(log 4)=(log y)log 3 Rightarrow

(ii) From

(i) (log 4)^ 2 -(log 3)^ 2 =log 3 log x-log4 logy Rightarrow(mi) From

(ii) log x log 3 = log y log 4 = lambda(say) Rightarrow

(iv) From (iv) and

(iii) (log 4) ^ 2 - (log 3) ^ 2 = [(log 3) ^ 2 - (log 4) ^ 2] lambda;

lambda =

- 1; log x =

- log 3 = log 1/3; Rightarrow logy=

-log 4=log 1 4;

therefore x= 1 3 ,y= 1 4

Hence, Verification complete

Note :-

Remember it's easy just we have to subtract it.

____________________________

$\sf\red{Thank\:you!}$

${\huge{\underline{\small{\mathbb{\pink{Hope \ it's \ clear \ Thanks♡}}}}}}$

$\sf\red{Be\:Brainly<3}$

${\huge{\underline{\small{\mathbb{\pink{Be \ happy \ stay \ blessed♡}}}}}}$

Answer 2

Answer:

Answer is in the attachment.

Hope my answer was helpful.