Solve for x in each of the following.

Question

If log_x 128 =4/6, then x =

Answer 1

Log_x128 = 4/6

 

log_x128 = 2/3

 

 

The solution to a logarithm is the exponent of the log's base number.

 

x^2/3 = 128

 

 

Raise both sides of equation by the power of 3/2 to undo the exponent on the left side.

 

(x^2/3)^3/2 = (128)^3/2

 

 

x = (128)^3/2

 

 

According to the rules of radicals and exponents.

 

x^m/n  =  ⁿ√(x^m)

 

 

x = √(128³)

 

x = √(128²) √(128)

 

x = 128 √(128)

 

x = 128 √(64) √(2)

 

x = 128 * 8 √(2)

 

x = 1024√(2)