Question

How do you write the logarithmic expressions as a single logarithm `2log_2)6 - 4)log_2y`?

Answer 1

This expression can be written as `log_2(36/y^4)`

Explanation:

I assume that the brackets are here just by mistake because there are only closing brackets, so the correct expression is:

`2log_2 6- 4log_2 y`

This expression can be rewritten as follows:

`2log_2 6- 4log_2 y=log_2 6^2-log_2 y^4=log_2 (36/y^4)`

The first step uses the property of logarythms which says that:

`n*log_a b=log_a b^n` ##

The last step uses the property which says that:

`log_a b - log_a c=log_a(b/c)`