Question

find x if whole root of (6⁰ + 1/3);= (0.75)^2x-3​

Answer 1

Step-by-step explanation:

We should know,

(a^m)^n = a^(mn)

a⁰ = 1

a^(-1) = 1/a

also, 0.75 = 75/100 = 3/4

If your Question is

√(6⁰ + (1/3) = (0.75)^(2x - 3)

Squaring both sides we get

6⁰ + (1/3) = ((3/4)^(2x - 3))^2

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

(3/3) + (1/3) = (3/4)^(4x - 6)

(3 + 1)/3 = (3/4)^(4x - 6)

(4/3) = (3/4)^(4x - 6)

(3/4)^(-1) = (3/4)^(4x - 6)

Thus, the bases are equal

so, -1 = 4x - 6

4x = 5

x = 5/4

Now,

If your Question is

√(6⁰) + 1/3 = (0.75)^(2x - 3)

√1 + 1/3 = (3/4)^(2x - 3)

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

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

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

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

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

Now bases are equal

thus,

-1 = 2x - 3

2x = 2

x = 2/2 = 1

x = 1

Hope you understood it........All the best