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What is the value of log_5(125)?
What is the value of log_5(125)?
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What is the value of log_5(125)?
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log_5(125) = log_5(5^3) = 3.
Questions & Step-by-step Solutions
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Q: What is the value of log_5(125)?
Solution:
log_5(125) = log_5(5^3) = 3.
Steps: 6
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Step 1: Understand what log_5(125) means. It asks, 'To what power must we raise 5 to get 125?'
Step 2: Recognize that 125 can be written as a power of 5. Specifically, 125 is equal to 5 multiplied by itself three times: 5 * 5 * 5, which is 5^3.
Step 3: Rewrite the logarithm using this power: log_5(125) = log_5(5^3).
Step 4: Use the property of logarithms that states log_b(b^x) = x. Here, b is 5 and x is 3.
Step 5: Apply this property: log_5(5^3) = 3.
Step 6: Conclude that the value of log_5(125) is 3.
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