We're working with logarithms of base 3

In summary, logarithms of base 3 are a type of mathematical operation that is used to find the exponent or power to which the base of 3 must be raised to produce a given number. They are commonly used because they are a convenient base for many calculations and have various real-world applications. The main difference between logarithms of base 3 and other bases is the number used as the base, and they can be solved using logarithm properties and basic algebraic rules. Alternatively, you can use a calculator or online logarithm solver.
  • #1
tharock220
4
0

Homework Statement


We're working with logarithms of base 3, and log(4)=a and log(7)=b.
The goal is to put log(21) in terms of a and b. For example, take the log(112). It's the same thing as 2a+b since 4*4*7 = 112.


Homework Equations



Just the standard log properties.

The Attempt at a Solution



The only thing I could come up with is 1 + b log(3) = 1. I've been using Matlab to try to figure out a way to create 21 using a product and/or quotient of powers of 7 and 3 but have been unable to do so.
 
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  • #2


21 = 3 * 7, and you know log(7) and log(3).
 

FAQ: We're working with logarithms of base 3

1. What are logarithms of base 3?

Logarithms of base 3 are a type of mathematical operation that is used to find the exponent or power to which the base of 3 must be raised to produce a given number. In other words, it is the inverse function of raising 3 to a certain power.

2. Why is base 3 commonly used in logarithms?

Base 3 is commonly used in logarithms because it is a convenient base for many calculations and has several important applications in mathematics and science. It is also one of the smallest bases that can be used to represent all positive numbers.

3. How are logarithms of base 3 different from other bases?

The main difference between logarithms of base 3 and other bases is the number that is used as the base. Logarithms of base 3 are calculated by dividing the logarithm of a number by the logarithm of 3, while other bases use a different number as the base.

4. What are some real-world applications of logarithms of base 3?

Logarithms of base 3 have many real-world applications, such as in music theory, acoustics, and electronics. They are also commonly used in computer science and data analysis to represent and manipulate large numbers in a more manageable way.

5. How can I solve logarithms of base 3 equations?

To solve logarithms of base 3 equations, you can use the properties of logarithms and basic algebraic rules. First, rewrite the equation in exponential form, then use the rules of logarithms to simplify the equation and solve for the variable. Alternatively, you can use a calculator or online logarithm solver to find the solution.

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