Evaluating a logarithmic expression

Text

Compute the value of $E=\log_2 32+\log_3\dfrac{1}{9}-\log_5 1$.

Solution

Use the definition of logarithm term by term:

• $\log_2 32=\log_2 2^{5}=5$;
• $\log_3\tfrac19=\log_3 3^{-2}=-2$;
• $\log_5 1=0$.

Hence $E=5+(-2)-0=3$. $\boxed{\,E=3\,}$