find the values of the following expression

Consider the numbers separately

First log(base 4) 2

log(base 4) 2
= log (base 4) [4^(1/2)]
= 1/2

(The last step is by basic definition of logarithm)

(If you write it down nicely you'll know!)

Then consider

log(base 1) 18. However, this is undefined.
Maybe you have had some mistakes in your question...

Same goes to 2log (base 4) (3/2). It CANNOT BE COMPUTED without using calculator.

But the general idea is like my first step. You will know and understand it easily once you follow my first step.

Hope I can help you!


P.S. If it is log 42 instead of log (base 4) 2, then it can be computed using law of logarithms.