Maths SURDS and INDICES problems?

Question

Solve

1)(√3)x = x + √3

2)2+(√3) x= x/√3

3) (1/√2)+x= x/√2

4) (27x^-3)/2 = 1

5) (2x^3) - 128 =0

6) (32x^-3) = (√x)/4

7) 5 * 5^x = 25 ^x^2

Answer 1

The equation is (27x^-3) / 2 = 1.

Multiply each side by 2.

[(27x^-3) * 2] / 2 = 1 * 2

27x^-3 = 2

Apply Property of negative exponent: a^-m = 1/ a^m.

27 / x³ = 2

Multiply each side by x³.

27 * x³ / x³ = 2 * x³

27 = 2x³

Divide each side by 2.

27 / 2 = x³

x³ = 27 / 2

Apply cube root on both sides.

∛(x³) = ∛(27 / 2)

x = ∛(27 / 2)

x = ∛(27) / ∛(2)

x = ∛(3³) / ∛(2)

x = 3 / ∛(2).