7^2+log 7 3 (семь в степени 2+ логарифм числа 3 по основанию 7)

To solve the expression $7^{2+{\log }_{7}3}$, we use the properties of exponents and logarithms. Solution Steps

1. Use the Product Rule of Exponents
   The rule states that $a^{m+n}=a^m\cdot a^n$. We can split the expression into two parts:
   $7^{2+{\log }_{7}3}=7^2\cdot 7^{{\log }_{7}3}$ Calculate the First Part
   The first term is a simple power:
   $7^2=49$ Simplify the Second Part
   Using the identity $a^{{\log }_{a}x}=x$ (the definition of a logarithm), we simplify the second term:
   $7^{{\log }_{7}3}=3$ Multiply the Results
   Now, substitute the values back into the expression:
   $49\cdot 3=147$

Final Answer: 147 Would you like me to solve another logarithmic expression or provide a breakdown of the specific properties used?