Given:
Consider the expression is
[tex]\log_63+\log_68-\log_64[/tex]
To find:
The value of given expression.
Solution:
We have,
[tex]\log_63+\log_68-\log_64[/tex]
Using properties of logarithm, we get
[tex]=\log_6(3\times 8)-\log_64[/tex] [tex][\because \log_am+\log_an=\log_amn][/tex]
[tex]=\log_6(24)-\log_64[/tex]
[tex]=\log_6\left( \dfrac{24}{4}\right)[/tex] [tex][\because \log_am-\log_an=\log_a\dfrac{m}{n}][/tex]
[tex]=\log_66[/tex]
[tex]=1[/tex] [tex][\because \log_aa=1][/tex]
Therefore, the value of given expression is 1.
