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

In summary, the conversation is about finding the value of 10^-10log3, with the question of whether the logarithm is base 10 or not. The conversation also mentions the use of parentheses and the properties of logarithms.
  • #1
ohhnana
25
0

Homework Statement



10^-10log3

Homework Equations





The Attempt at a Solution


(3)10^-10log
 
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  • #2
Your first expression doesn't mean much until you add some parentheses. Your solution means even less. What the numerical value of 'log'??
 
  • #3
that's the question that was given , I'm guessing the log value is 10
 
  • #4
it's telling me to find the value
 
  • #5
You're not listening -- you need parentheses. Do you mean
[tex]10^{-10\log 3}[/tex]
or
[tex]10^{-10}\log 3[/tex]
or neither?
 
  • #6
i mean [tex]
10^{-10\log 3}
[/tex]
 
  • #7
Use the properties of logarithms.
For starters, log ab = b * log a
 
  • #8
Is that logarithm base 10?
 
  • #9
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.
 

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

What is the value of the logarithm?

The value of the logarithm is the exponent to which a fixed number, called the base, must be raised to produce a given number.

Why is the value of the logarithm important?

The value of the logarithm is important because it allows us to solve exponential equations, convert between different number bases, and perform calculations involving very large or very small numbers.

How is the value of the logarithm calculated?

The value of the logarithm is calculated by using a logarithm function, which is the inverse of an exponential function. The most common logarithm functions use base 10 (log base 10) or base e (natural log) to calculate the value.

What is the relationship between logarithms and exponents?

The relationship between logarithms and exponents can be expressed as: log base b (x) = y if and only if b^y = x. In other words, the logarithm tells us what exponent we need to raise the base to in order to get the given number.

What are some real-life applications of logarithms?

Logarithms are used in many fields of science and technology, including finance, biology, physics, and engineering. They are commonly used for measuring the magnitude of earthquakes, calculating pH levels in chemistry, and analyzing population growth. In finance, logarithms are used to calculate compound interest and for risk analysis.

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