Use the properties of logs to show that 1/3+ log_2(cube root of 10) and log _2(cube root of 20) are equivalent

Question

Start with one side and show each step to get to the other one.

 

Thank you!

Answer 1

Things to remember about the properties of logs:

 

1) the coefficient of logs becomes the exponent of the logs argument and vice versa.

2) the product of the log's argument is the addition of logs.

3) the quotient of the log's argument is the difference of logs.

 

 

(1/3) + log₂ ³√(10) = (1/3) + log₂(10^1/3)

 

                             = (1/3) + (1/3)log₂(10)

 

 

 

 

log₂ ³√(20) = log₂(20^1/3)

 

                 = (1/3)log₂(20)

 

                 = (1/3)[log₂(2 * 10)]

 

                 = (1/3)[log₂(2) + log₂(10)]

 

                 = (1/3)log₂(2) + (1/3)log₂(10)

 

                 = (1/3) + (1/3)log₂(10)