## anonymous one year ago 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!

1. anonymous

$\log_{3} \sqrt{27}$

2. anonymous

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

3. anonymous

Can you explain why you did that?

4. anonymous

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 $$log_3 3^{\frac{3}{2}}=\frac{3}{2}$$