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If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by?
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If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y ...
Solution:
Simplifying the left-hand side, we get:
9^y . 3^2 . (3^(-y))^(-1) - 27^y . 3^3x . 2^3 = 1/27
= 3^(2y) . 3^(-y) - 3^(3x+y) . 2^3
= 3^(2y-y) - 2^3 . 3^(3x+y)
= 3^y - 8 . 3^(3x+y)
= 3^y(1 - 8 . 3^(2x))
Now, we have:
1/27 = 3^(-3)
So, we can write:
3^y(1 - 8 . 3^(2x)) = 3^(-3)
Taking logarithm on both sides, we get:
y log 3 + log(1 - 8 . 3^(2x)) = -3 log 3
Subtracting log(1 - 8 . 3^(2x)) from both sides, we get:
y log 3 = -3 log 3 - log(1 - 8 . 3^(2x))
Dividing by log 3, we get:
y = -3 - (1/log 3) . log(1 - 8 . 3^(2x))
Now, we know that:
x-y = x - (-3 - (1/log 3) . log(1 - 8 . 3^(2x)))
= x + 3 + (1/log 3) . log(1 - 8 . 3^(2x))
Hence, x-y is given by x + 3 + (1/log 3) . log(1 - 8 . 3^(2x)).
Note: The solution involves simplifying the left-hand side of the given equation and then taking logarithm on both sides to isolate y. Finally, using the value of y, we can find x-y.
Simplifying the left-hand side, we get:
9^y . 3^2 . (3^(-y))^(-1) - 27^y . 3^3x . 2^3 = 1/27
= 3^(2y) . 3^(-y) - 3^(3x+y) . 2^3
= 3^(2y-y) - 2^3 . 3^(3x+y)
= 3^y - 8 . 3^(3x+y)
= 3^y(1 - 8 . 3^(2x))
Now, we have:
1/27 = 3^(-3)
So, we can write:
3^y(1 - 8 . 3^(2x)) = 3^(-3)
Taking logarithm on both sides, we get:
y log 3 + log(1 - 8 . 3^(2x)) = -3 log 3
Subtracting log(1 - 8 . 3^(2x)) from both sides, we get:
y log 3 = -3 log 3 - log(1 - 8 . 3^(2x))
Dividing by log 3, we get:
y = -3 - (1/log 3) . log(1 - 8 . 3^(2x))
Now, we know that:
x-y = x - (-3 - (1/log 3) . log(1 - 8 . 3^(2x)))
= x + 3 + (1/log 3) . log(1 - 8 . 3^(2x))
Hence, x-y is given by x + 3 + (1/log 3) . log(1 - 8 . 3^(2x)).
Note: The solution involves simplifying the left-hand side of the given equation and then taking logarithm on both sides to isolate y. Finally, using the value of y, we can find x-y.
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If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by?
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If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by?.
If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 9^ y .3^ 2 .(3 ^ (- y)) ^ - 1 - 27 ^ y3^ 3x .2^ 3 = 1/ 27 then x-y is given by?.
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