Now, let's rewrite the equation with the simplified exponents:
1/(3^(4x-3)) + 6^(-3x+1) = 2^(2x^2-3)
Now, we need to choose an approach to solve for x. We can take the logarithm on both sides, or we could try to simplify further. Let's first try to simplify further:
1/(3^(4x-3)) + 6^(-3x+1) = 2^(2x^2-3)
1/(3^(4x) 3^(-3)) + 1/6^(3x) = 1/2^(3) 2^(2x^2)
3^3/3^(4x) + 1/6^(3x) = 1/2^(3) * 2^(2x^2)
27/3^(4x) + 1/6^(3x) = 1/8 * 2^(2x^2)
((276^3)/3^(4x)) + 1/6^(3x) = 1/8 2^(2x^2)
Now we can simplify further or take the logarithm on both sides.
First, let's simplify the exponents:
3^(2x-6x+3) = 3^(-4x+3) = 1/(3^(4x-3))
6^(x^2-3x+1) = 6^(-3x+1)
2^(2x^2-6+3) = 2^(2x^2-3)
Now, let's rewrite the equation with the simplified exponents:
1/(3^(4x-3)) + 6^(-3x+1) = 2^(2x^2-3)
Now, we need to choose an approach to solve for x. We can take the logarithm on both sides, or we could try to simplify further. Let's first try to simplify further:
1/(3^(4x-3)) + 6^(-3x+1) = 2^(2x^2-3)
1/(3^(4x) 3^(-3)) + 1/6^(3x) = 1/2^(3) 2^(2x^2)
3^3/3^(4x) + 1/6^(3x) = 1/2^(3) * 2^(2x^2)
27/3^(4x) + 1/6^(3x) = 1/8 * 2^(2x^2)
((276^3)/3^(4x)) + 1/6^(3x) = 1/8 2^(2x^2)
Now we can simplify further or take the logarithm on both sides.