# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_3 73?

Jul 9, 2015

${\log}_{3} 73 \approx 3.095$

#### Explanation:

The Change of Base Formula says that:

${\log}_{a} x = {\log}_{b} \frac{x}{\log} _ b a$

Calculators don't have ${\log}_{3} x$ button, but they have "log" which is base 10 logarythm and "ln" which is natural logarythm (base $e$), so you can use this formula in such a way (using base 10 log):

1) Calculate $\log 3$
2) Put the result in memory (button "X->M" or simmilar)
3) Calculate $\log 73$
4) Press divide button
5) Recall memory result (button "RM" or simmilar)
6) Press result (=) button.

Note: Using "ln" instead of "log" is also possible.