Question

Solve for x:
(8/3)^3-x=(3/8)^2x-1
Answer must be x=-2

Answer 1

Hello Mate!

( 8/3 ) ^ ( 3 - x ) = ( 3/8 )^ ( 2x - 1 )

Now reciprocal 1st term

( 3/8 )^ -( 3 - x ) = ( 3/8 )^( 2x - 1 )

As bases are common,

-3 + x = 2x - 1
-3 + 1 = 2x - x
-2 = x

Hope it helps☺!✌

Answer 2

(8/3)^(3-x) = (3/8)^(2x-1)
The equations are reciprocal to each other
If base are equal power should be added..
(3-x)= 1/(2x-1)
(3-x)(2x-1)=1
(6x-3-2x^2+x)=1
solving the quadratic equation,

we get x=-2 and x=1