# How do you calculate log_4 3.6 with a calculator?

Sep 3, 2016

#x = log3.6/log4 = 0.924

#### Explanation:

${\log}_{4} 3.6$

In this log form, the question being asked is
"what index/power of 4 will give 3.6?"

As 3.6 is not one of the exact powers of 4, we will need a calculator.
Let's estimate first....

${4}^{1} = 4$, so the answer should be just less than 1.

Log form and index form are interchangeable.

${\log}_{a} b = c \text{ "hArr" } {a}^{c} = b$

${\log}_{4} 3.6 = x \text{ "hArr" } {4}^{x} = 3.6$

$\log {4}^{x} = \log 3.6 \text{ "larr" log both sides}$

$x \log 4 = \log 3.6$

$x = \log \frac{3.6}{\log} 4 = 0.924 \text{ "larr" the is what we expected}$