Question

-Picture attached-‼️‼️ 35 pnts for these all to get done plz and thnx whoever gets them done in a day or so, will receive a five star and a thanks from me to u

Answer 1

Explanation:

1) 4 (2x+3)=1

(42x)*43= 1

64*42x=1

Taking Log to the base 2 to solve

log2(64*42x)

By property of ln

log2 (xy)= log2 x + log2 y

Therefore,

= log2 (64)+ log2 (42x)

log2 (64) =6 and by Property log2 (xn) = n logb x.

= 6 + 2x log2 4

= 6 + 2x (2)

Putting above equation equal to 0 to get the value of x

6 + 4x = 0

4x = -6

x = - 6/4

x= -3/2

Putting value of x in given equation

(42x)*43= 1

64 * 4(2*(-3/2)) =1

43 * 4-3 = 1

64/64 =1

1=1

2) 81 * 9(-2b-2) = 27

81 * 9-2b * 9-2 = 27

9-2 = 81

(81/81) * 9-2b =27

9-2b = 27

(32)-2b = 33

3-4b = 33

-4b=3

b= -3/4

Putting b’s value in given equation

81 * 9(-2b-2) = 27

81 * 9((-2*-3/4)-2) =27

(81/81) * 9 3/2 = 27

9 3/2 = 27

27 = 27

3) 31-2x = 243

3 * 3-2x =243

3-2x =243/3

3-2x = 81

3-2x = 34

-2x = 4

x = -2

putting the value of x in given equation

31-2(-2) = 243

31+4= 243

35= 243

243 =243

4) 43X-2 = 1

43X * 4-2 = 1

43X / 42 = 1

43X / 16 = 1

43X = 16

3x = 2

X=2/3

Putting value of x in given equation

4(3*2/3)-2 = 1

42-2 =1

40 =1

1=1

5) (1/6) (3x+2) * 216 3x = 1/216

216 = 63

6 (-3x-2) * 216 3x = 1/216

6 (-3x) * 6-2 * 216 3x = 1/63

6 (-3x) * (63)3x = 6-3/6-2

6 (-3x) * 69x = 6-3 * 62

69x-3x = 6(-3+2)

66x = 6-1

6x = -1

x=-1/6

Putting value of x in given equation

(1/6) (3*-1/6+2) * 216 3*-1/6 = 1/216

(1/6) (-1/2+2) * 216 -1/2 = 1/216

(1/6) ((-1+4)/2) * 216 -1/2 = 1/216

(1/6) (3/2) * (63)-1/2 = 1/216

6-3/2 * 6-3/2 = 1/216

6 (-3/2-3/2) = 1/216

6 (-6/2) = 1/216

6 (-3) = 1/63

6 (-3) =6 (-3)