Question

3^x=9 3^y, 8 2^y-4^x,solve for x and y​

Answer 1

3,ki power x = 9

3power x = 3²

x=2 because base same hoti h to power equal ho jati h

Answer 2

The value of x = 1

The value of y = -1

Step-by-step explanation:

Given :-

3^x=9 3^y, 8 2^y=4^x

To find:-

solve for x and y

Solution:-

Given that

3^x = 9 3^y

=>3^x /3^y=3²

since a^m/a^n=a^(m-n)

=>3^(x-y)=3²

Since bases are equal then exponents must be equal

x-y=2

y=x-2-------(1)

and

8×2^y = 4^x

=>2³×2^y = (2²)^x

since a^m×a^n= a^(m+n)

=>2^(3+y)=2^2x

Since bases are equal then exponents must be equal

3+y=2x

=>3+x-2=2x

=>1+x=2x

=>2x-x=1

x=1

from (1)

y=1-2

y=-1

Answer:-

The value of x = 1

The value of y = -1

Check:-

1)If x=1 and y=-1 then

3¹=9(3-¹)

=>3=9/3

=>3=3verified

2) 8(2-¹)=4¹

since a^-n=1/a^n

8/2=4

4=4

verified