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To evaluate the equation  log7 343 (with base 7) , we pattern this to its standard form log a b (with base a). this expression is equal to log b over log a. In this case, the expression given is equal to log 343 / log 7. The answer to this problem is 3. 3^7 is equal to 343.

Answer:  The required value of the given expression is 3.

Step-by-step explanation:  We are given to evaluate the following logarithmic expression :

\(E=\log_7343~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)

We will be using the following logarithmic properties :

\((i)~\log_ab^c=c\log_ab,\\\\(ii)~\log_aa=1.\)

From (i), we get

\(E\\\\=\log_7343\\\\=\log_77^3\\\\=3\log_77~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using property (i)}]\\\\=3\times1~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Using property (ii)}]\\\\=3.\)

Thus, the required value of the given expression is 3.

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