Given:
[tex]log_43+log_48-log_46[/tex]
To Determine: The value of the given expression
Solution
Let us apply the logarithm rule below
[tex]\begin{gathered} logA+logB=log(A\times B) \\ So \\ log_43+log_48=log_4(3\times8)=log_424 \\ log_43+log_48-log_46=log_424-log_46 \end{gathered}[/tex]
Applying the rule below again
[tex]\begin{gathered} logA-logB=log(A\div B) \\ So, \\ log_424-log_46=log_4(24\div6)=log_44 \end{gathered}[/tex]
And finally applying the rule below
[tex]\begin{gathered} log_aa=1 \\ Then \\ log_44=1 \end{gathered}[/tex]
Hence, the solution of the given expression is 1, OPTION A
