Logarithmic Help: Solving for z, m & n

In summary, to solve for z in a logarithmic equation, isolate the logarithmic term, use the exponential form of logarithms, and then solve for z by taking the logarithm of both sides. The difference between a common logarithm and a natural logarithm is that a common logarithm uses 10 as the base while a natural logarithm uses e. To solve for m and n in a logarithmic equation, use the properties of logarithms and algebraic methods. Yes, a calculator can be used to solve logarithmic equations, but make sure to check the manual for instructions. Common mistakes to avoid when solving logarithmic equations include not applying properties, using the wrong base, and making calculation errors. It is crucial to double check
  • #1
stosw
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0

Homework Statement



http://img20.imageshack.us/img20/1476/mathproblemi.jpg [Broken]


Homework Equations



Properties of logs.

The Attempt at a Solution



For the first two I did:

Int( [tex]\frac{Log(2)}{Log(1.1)}[/tex] )

Doing this resulted in the correct answers for the first two boxes. When I try similar techniques to solve for z, m,n I get incorrect answers.

Anyone have tips or suggestions on how to go about finding these?
 
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  • #2
Your task is to approximate 2 and 3 as 1.1^N and 1.1^M, and solve z from there.
 
  • #3
If [itex]1.1^7[/itex] is approximately 2 then [itex]2^x[/itex] is approximately [itex](1.1^7)^x= 1.1^{7x}[/itex]. That's the point of this exercise.
 

1. How do I solve for z in a logarithmic equation?

To solve for z, you will need to use the properties of logarithms. First, isolate the logarithmic term on one side of the equation. Then, use the exponential form of logarithms to rewrite the equation. Finally, solve for z by taking the logarithm of both sides of the equation.

2. What is the difference between a common logarithm and a natural logarithm?

A common logarithm, also known as base 10 logarithm, uses 10 as the base of the logarithm. A natural logarithm, on the other hand, uses e as the base of the logarithm. The value of e is approximately 2.71828.

3. How do I solve for m and n in a logarithmic equation?

To solve for m and n, you will need to use the properties of logarithms. First, isolate the logarithmic term on one side of the equation. Then, use the properties of logarithms to rewrite the equation and combine like terms. Finally, solve for m and n by using algebraic methods.

4. Can I use a calculator to solve logarithmic equations?

Yes, most scientific calculators have a logarithm function that you can use to solve logarithmic equations. Make sure to check your calculator's manual for instructions on how to use the logarithm function.

5. What are the common mistakes to avoid when solving logarithmic equations?

Some common mistakes to avoid when solving logarithmic equations include forgetting to apply the properties of logarithms, using the wrong base for the logarithm, and making calculation errors. It's important to double check your work and make sure you are following the correct steps.

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