In this question each stage of your working must be shown and must not contain a logarithm. Simplify 1/2 log2 36+ 2 log2 8 - log2 24.

Question

In this question each stage of your working must be shown and must not contain a logarithm.

Simplify
1/2 log2 36+ 2 log2 8 - log2 24.

Answer 1

log₂36^1/2 + log₂8² - log₂24 = log₂[(6)(64)/24] = log₂16 = log₂2⁴ = 4

Answer 2

I am assuming the logs have a common base of 2.

 

(1/2)log₂36 + 2log₂8 - log₂24

 

 

To simplify, we apply the properties of logs.

 

The coefficient of logs is the exponent of the log's arguments.

The sum of logs is the product of the log's arguments.

The difference of logs is the quotient of the log's arguments.

 

 

log₂√(36) + log₂64 - log₂24 =

 

log₂6 + 6 - log₂24 =

 

6 + log₂(6 / 24) =

 

6 + log₂(1/4)

 

 

Now that we compacted all the log terms to a single log term and rational number, we need to apply the properties of logs to convert the log term to an equivalent rational number.  I believe your final answer cannot contain a logarithm.

 

6 + log₂1 - log₂4 =

 

6 + 0 - 2 =

 

4