4 x = 2 3 y Solve for x from the equation above.
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The given equation is 4 x = 2 3 y which can be further written as 4 x = ( 2 3 y ) 1 / 2 . Using the power rule , the equation becomes 4 x = 2 3 y / 2 . To make the bases equal we can write the equation as 2 2 x = 2 3 y / 2 . Now as we have the bases equal, the exponents too must be equal for the equation to be correct. Hence we have 2 x = 2 3 y ⇒ x = 4 3 y . □
Standard approach of simplifying the exponents into a common term.
4 x = 2 3 y
4 x = ( 2 3 y ) 2 1
4 x = ( 4 ) 2 3 y
4 x = ( 4 2 1 ) 2 3 y
4 x = 4 2 3 y × 2 1
4 x = 4 4 3 y
x = 4 3 y
4^x = √(2^[3y])
4^(2x) = 2^(3y)
2^(4x) = 2^(3y)
The same base
4x = 3y
x = 3y / 4
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4 x 2 2 x ⇒ 2 x x = 2 3 y = 2 2 3 y = 2 3 y = 4 3 y