log5 1
Understand the Problem
The question is asking for the value of log base 5 of 1. In logarithmic terms, we want to know what exponent we raise 5 to in order to get 1.
Answer
$\log_5(1) = 0$
Answer for screen readers
The final answer is $\log_5(1) = 0$.
Steps to Solve
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Understanding Logarithms In logarithmic terms, we want to find $x$ in the equation $5^x = 1$.
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Recall a Key Property of Exponents We know that any non-zero number raised to the power of 0 equals 1. Therefore, we can conclude: $$ 5^0 = 1 $$
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Setting Up the Equation Since $5^x = 1$, we can replace 1 with $5^0$. This gives us the equation: $$ 5^x = 5^0 $$
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Equate the Exponents Since the bases are the same, we can set the exponents equal to each other: $$ x = 0 $$
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Final Answer The value of $\log_5(1)$ is therefore 0.
The final answer is $\log_5(1) = 0$.
More Information
In logarithmic terms, this means that raising 5 to the power of 0 results in 1. This is a fundamental property of logarithms and exponents.
Tips
Common mistakes include confusing the logarithm of 1 with the logarithm of other numbers. Remember, the logarithm of any positive number is 0 if you're taking the logarithm of 1, regardless of the base.
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