Answer
$0.8982.$
Work Step by Step
${{\log }_{6}}5$
Now, use the change of base formula:
${{\log }_{a}}x=\frac{{{\log }_{b}}x}{{{\log }_{b}}a}$
It is always assumed that the log means ${{\log }_{10}}$.
Thus,
${{\log }_{6}}5=\frac{\log 5}{\log 6}$
The answer can be calculated by using a Ti-84:
Step1: Press ON key.
Step2: Press LOG key.
Step3: Enter the value 5.
Step4: Press “)” key.
Step5: Press “$\div $ ” key.
Step6: Press LOG key.
Step7: Enter the value 6.
Step8: Press ENTER key.
The result obtained is 0.8982.
Thus,
${\log \left( 5 \right)}/{\log \left( 6 \right)}\;\approx 0.8982$
