Need help solving these log equations

Question

Solve

 

1. log₁₆x=3/2

 

2.log_x81 = 3

 

3. Log₂1/8 = x

 

thanks 

 

Answer 1

1. Log₁₆X=3/2

 

16^(3/2) = X

 

X = (4²)^(3/2)

 

X = 4^(2*3/2)

 

X =4³

 

X =64

 

 

2. Log_x81=3

 

X³ = 81

 

X³ = 3⁴

 

X = (3⁴)^(1/3)

 

X = 3^(4/3)

 

X = 4.327

 

 

 

3. Log₂1/8 = X

 

2^X = 1/8

 

2^X = 2^-3

 

X = -3

 

 

 

 

Answer 2

 

(1)

     Log₁₆ x = 3/2

 

     16^3/2 = x

 

     √(16)³ = x

 

     √(4²)³  = x

 

     √(4³)²  =x

 

     4³ = x

 

     64 = x

 

(2)  Log_x81 = 3

 

     x³ = 81

 

     x = 81^1/3

 

     x = (3⁴)^1/3

 

     x = 3^4/3

 

     x = 3^3/3 • 3^1/3

 

     x = 3 • 3^1/3

 

(3)  Log₂1/8 = x

 

      Log₂2^-3 = x

 

      -3•Log₂2 = x

 

      -3 (1) = x

 

      -3 = x

Answer 3

1. 16^(3/2)=x

    (2^4)^(3/2)=x

    (2^6)=x

    64=x

 

2. x^3=81

    take the cube root of both sides

    x=(81)^(1/3

    x=(27*3)^(1/3)

    27 is a cube

    x=3(3^[1/3])

    x=4.3267

 

3. log(2)*2^[-3]=x

    -3log(2)2=x

    -3(1)=x

    -3=x