• If $$\Large 3^{x+y}=81$$ and $$\Large 81^{x-y}=3$$, then what is the value of x?
 A) $$\Large \frac{17}{16}$$ B) $$\Large \frac{17}{8}$$ C) $$\Large \frac{17}{4}$$ D) $$\Large \frac{15}{4}$$

 B) $$\Large \frac{17}{8}$$

Given,

$$\Large 3^{x+y}=51$$

= $$\Large 3^{x+y}=3^{4}$$

= x + y = 4 ...(i)

and $$\Large 81^{x-y}=3 \ or \ \left(3^{4}\right)^{x-y}=3^{1}$$

= $$\Large x-y = \frac{1}{4}$$ ...(ii)

On solving the Eqs. (i) and (ii), we get

$$\Large 2x = \frac{17}{4} = x = \frac{17}{8}$$

##### Similar Questions
1). Ten chairs and six tables together cost Rs.6200, three chairs and two tables together cost Rs.1900. The cost of 4 chairs and 5 tables is
 A). Rs.3000 B). Rs.3300 C). Rs.3500 D). Rs.3800
2). The system of equations 3x + y - 4 = 0 and 6x + 2y - 8 = 0 has
 A). a unique solution x = 1, y=1 B). a unique solution x = 0, y = 4 C). no solution D). infinite solutions
3). If x+ y - 7 = 0 and 3x + y -13 = 0, then what is $$\Large 4x^{2} + y^{2} + 4xy$$ equal to?
 A). 75 B). 85 C). 91 D). 100
4). The solution of the equations $$\Large \frac{p}{x}+\frac{q}{y} \ and \ \frac{q}{x}+\frac{p}{y}$$ n is
 A). $$\Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq}$$ B). $$\Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq}$$ C). $$\Large x=\frac{p^{2}-q^{2}}{mp-nq}, y=\frac{p^{2}-q^{2}}{np-mq}$$ D). $$\Large x=\frac{q^{2}-p^{2}}{mp-nq}, y=\frac{q^{2}-p^{2}}{np-mq}$$
5). If $$\Large \frac{3}{x+y}+\frac{2}{x-y}=2$$ and $$\Large \frac{9}{x+y}-\frac{4}{x-y}=1$$, then what is the value of $$\Large \frac{x}{y}$$?
 A). $$\Large \frac{3}{2}$$ B). 5 C). $$\Large \frac{2}{3}$$ D). $$\Large \frac{1}{5}$$
6). If $$\Large \frac{a}{b}-\frac{b}{a}=\frac{x}{y}$$ and $$\Large \frac{a}{b}+\frac{b}{a}= x - y$$ , then what is the value of x?
 A). $$\Large \frac{a+b}{a}$$ B). $$\Large \frac{a+b}{b}$$ C). $$\Large \frac{a-b}{a}$$ D). None of these
7). If $$\Large \frac{x}{2}+\frac{y}{3}=4$$ and $$\Large \frac{2}{x}+\frac{3}{y}=1$$ then what is x + y equal to?