Question

can someone explain how to find these without using a calculator? my prof gave us answers to them but no explanations

Answer 1

I'll do the first one as an example

\(log_3 27=x\)
Definition of logarithmic

\(3^x=27\)
Find exponents with equal exponentials

\(3^{1x}=3^3\)
Cancel the exponentials, leaving you with powers

\(1x=3\)
Solve for x

\(x=\dfrac{3}{1}\)
\(x=3\)

Answer 2

thank you so much!