Is the Unspecified Base of a Logarithm Assumed to Be 10?

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The discussion centers on the expression 10^-10log3 and the ambiguity surrounding the base of the logarithm. Participants emphasize the importance of using parentheses to clarify the intended mathematical operation. There is a consensus that, in many contexts, an unspecified logarithm is assumed to be base 10. The properties of logarithms are referenced to aid in solving the expression. Overall, clarity in notation is crucial for accurate interpretation and calculation.
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Homework Statement



10^-10log3

Homework Equations





The Attempt at a Solution


(3)10^-10log
 
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Your first expression doesn't mean much until you add some parentheses. Your solution means even less. What the numerical value of 'log'??
 
that's the question that was given , I'm guessing the log value is 10
 
it's telling me to find the value
 
You're not listening -- you need parentheses. Do you mean
10^{-10\log 3}
or
10^{-10}\log 3
or neither?
 
i mean <br /> 10^{-10\log 3}<br />
 
Use the properties of logarithms.
For starters, log ab = b * log a
 
Is that logarithm base 10?
 
HallsofIvy said:
Is that logarithm base 10?

It's been my experience that, at this level, a logarithm without a specified base is generally the decimal logarithm.
 
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