Solving exponential equation

Question

125^2x * 25^x2-3  = ( √5)^x 

 

 

 

*The exponent of 25 is x squared btw. 

Answer 1

(125^2x)(25^x²-3) = (√5)^x

((5³)^2x)((5²)^x²-3)) = (5^1/2)^x     convert all to base 5

(5^6x)(5^(2x²-6) = 5^x/2                      laws of exponents

5^(2x² + 6x - 6) = 5^x/2                    powers of a product

2x² + 6x - 6 = x/2                            equal numbers of like bases have equal powers

4x² + 12x - 12 = x                           multiply both sides by 2

4x² + 11x - 12 = 0                          subtract x from both sides

 

The solutions to this quadratic are irrational.

Please check the accuracy of the equation.