Problem 42
Question
Evaluate each expression without using a calculator. $$7^{\log _{7} 23}$$
Step-by-Step Solution
Verified Answer
23
1Step 1 - Understand the properties of logarithms
According to the logarithm rules, if the base 'b' of the power is equal to the base 'b' of the logarithm, the power of the 'b' is equal to the logarithm's argument. Therefore, \(b^{\log _{b} x} = x\).
2Step 2 - Apply the rule to the given problem
Regarding the given expression \(7^{\log _{7} 23}\), it can be observed that the base of the power (7) equals the base of the logarithm (also 7). According to the rule explained in step 1, this power of the seven will be equal to the argument of the logarithm, which is 23.
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