Question

Solve x;. (8/27)^x-1=(9/4)^2x+1

Answer 1

Given: The term (8/27)^x-1=(9/4)^2x+1

To find: The value of x?

Solution:

• Now we have given (8/27)^x-1=(9/4)^2x+1

• We can rewrite it as:

                   (2/3)^3(x-1) = (3/2)^2(2x+1)

                   (2/3)^(3x-3) = (3/2)^(4x+2)

• Reciprocating the RHS side, we get:

                   (2/3)^(3x-3) = (2/3)^-(4x+2)

• Now equating the powers, we get:

                   3x - 3 = -4x - 2

                   7x = 1

                   x = 1/7

Answer:

              So the value of x is 1/7.

Answer 2

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