Evaluate the following expression.

Question

Can't figure this one out, thanks for any help !

 

log₂16√8

Answer 1

I assume you intended to place parentheses around 16√8.

 

log₂(16√8) = log₂16 + log₂√8

 

= 4 + log₂(8^1/2) = 4 + (1/2)log₂8

 

= 4 + (1/2)(3) = 4 + 3/2 = 11/2

Answer 2

Let           x = log₂16√8

 

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

 

2^x = 16√8

 

 

Convert to common base.

 

2^x = 2⁴(2³)^1/2

 

 

Apply rules of exponents.

 

2^x = 2⁴(2^3/2)

 

2^x = 2^{(8/2 + 3/2)}

 

2^x = 2^11/2

 

 

Now just equate the exponents.

 

x = 11/2