Solve this Exponential Function?

Favorite Answer

since the bases are the same, the exponents must also be equal, so

2x² = 5x - 2

now solve the resulting quadratic to get

x = 1/2 or x = 2


...also, if the base is 1 or 0 then you will also have solutions, so solve 3x-4=1 and 3x-4=0...Show more

x=2...Show more

Presentation, due to lack of brackets , is meaningless.
Can but GUESS that you mean :-

(3x - 4)^(2 x ²) = (3x - 4)^(5x - 2)

2x ² = 5x - 2
2 x ² - 5x + 2 = 0
( 2x - 1) (x - 2) = 0
x = 1/2 , x = 2

PS
In a subject such as this , should not have to guess ? !...Show more

http://www.wolframalpha.com/input/?i=%283x-4%29^%282x^2%29+%3D+%283x-4%29^%285x-2%29

x = 2
x = 1/2
x = 5/3
x = 4/3...Show more