Question

${3}^{x + y} = 81 \: and \: {81}^{x + y } = 3 \: has \: how \: many \: solutions \: and \: what \: is \: its \: solution$
please give step by step explaination​

Answer 1

Answer:

x = 15/8 y = 17/8

Step-by-step explanation:

we can put 81 = $3^4$

So $3^{(x+y)}$ = $3^4$  => x+y = 4 ...equation 1  (comparing the power with same base value)

Similarly for other equation : $81^{x+y} = 3^{4(x+y)} = 3^{(4x+4y)}$. hence as per 2nd given equation :

$3^{4x+4y} = 3^{1} => 4x+4y=1$ .... equation 2

now solve equation 1 and 2 will give x= 15/8 and y=17/8