Problem

Evaluate each expression.
(a) $\log _{9} 1=$
(b) $\log _{7} 49=\square$

Answer

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Answer

(b) \(\log _{7} 49= \boxed{2}\)

Steps

Step 1 :The logarithm is the inverse operation to exponentiation, just as subtraction is the inverse of addition and division is the inverse of multiplication. Logarithms are useful in many areas of science and engineering. The logarithm of a number x with respect to base b is the exponent to which b must be raised to yield x. In other words, the logarithm base b of a number x is the solution y to the equation \(b^y = x\).

Step 2 :Let's evaluate each expression.

Step 3 :(a) \(\log _{9} 1\)

Step 4 :The logarithm base 9 of 1 is asking what power we need to raise 9 to get 1. Any number raised to the power of 0 is 1. So, the answer should be 0.

Step 5 :(b) \(\log _{7} 49\)

Step 6 :The logarithm base 7 of 49 is asking what power we need to raise 7 to get 49. Since \(7^2 = 49\), the answer should be 2.

Step 7 :Final Answer:

Step 8 :(a) \(\log _{9} 1= \boxed{0}\)

Step 9 :(b) \(\log _{7} 49= \boxed{2}\)

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