Question

3. Write down the values of the following without using a calculator. Use your calculator to check your answers for those questions which use base 10.
(vii) log_3(square root 27)
I don't know what to do with this one, please help!

Answer 1

\[\log_{3} \sqrt{27}\]

Answer 2

\[\log_{3} \sqrt{27}=\log_{3}\sqrt{3^3}=\log_3(3^3)^{\frac{ 1 }{ 2 }}=\log_3 3^\frac{ 3 }{ 2 }\]

Answer 3

Can you explain why you did that?

Answer 4

because log and exponentials of the same base are inverses.
the \(log_3\) cancels the base of 3 in the exponential.

\(log_3 3=1\)
\(log_3 3^a=a\)

So for your problem
\(log_3 3^{\frac{3}{2}}=\frac{3}{2}\)