Simultaneous equations using exponential functions

In summary, simultaneous equations using exponential functions involve solving a set of equations with exponential terms simultaneously to find the values of the variables. Exponential functions are important in these equations because they represent relationships between variables that grow or decay at a constant rate, allowing for accurate modeling and prediction. To solve these equations, various methods such as substitution, elimination, or graphing can be used. Applications of these equations can be seen in fields such as finance, physics, and biology. Some common mistakes when solving them include forgetting to apply exponent rules, using the wrong substitution method, and making computational errors. It is important to double-check your work to avoid these errors.
  • #1
Wardlaw
27
0

Homework Statement



Solve the following equations using simultaneous equations

Homework Equations



32x[tex]\times[/tex]23y=17

4x[tex]\times[/tex]5y=37

Appologies for the bad equation set-up. The large 'x' is a multiplication sign.


The Attempt at a Solution


My attempt was to divide both of the equations together and then solve for x and y respectively, using the laws of logarithms.



 
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  • #2
What about taking the logarithm of both equations?

ehild
 
  • #3
Excellent suggestion!
 
  • #4
ehild said:
What about taking the logarithm of both equations?

ehild

Yes, i tried this. However the answer i get does not match the answer set in the textbook!
 
  • #5
Show your work.

ehild
 

FAQ: Simultaneous equations using exponential functions

What are simultaneous equations using exponential functions?

Simultaneous equations using exponential functions are a set of equations that involve exponential terms. These equations must be solved simultaneously to find the values of the variables.

Why are exponential functions important in simultaneous equations?

Exponential functions are important in simultaneous equations because they represent relationships between variables that grow or decay at a constant rate. This allows for accurate modeling and prediction of real-world phenomena.

How do you solve simultaneous equations using exponential functions?

To solve simultaneous equations using exponential functions, you can use a variety of methods such as substitution, elimination, or graphing. The key is to manipulate the equations to eliminate one variable and solve for the other.

What are some applications of simultaneous equations using exponential functions?

Simultaneous equations using exponential functions are used in various fields such as finance, physics, and biology. For example, they can be used to model compound interest, radioactive decay, and population growth.

What are some common mistakes when solving simultaneous equations using exponential functions?

Some common mistakes when solving simultaneous equations using exponential functions include forgetting to apply the exponent rules, using the wrong substitution method, and making computational errors. It is important to double-check your work to avoid these errors.

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