Solving for X: A Challenging Math Problem with Exponential Growth Rates

  • Thread starter EternityMech
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In summary, the conversation discusses a difficult math problem involving the equations 300 * 1.05x = 160 * 1.07x and the question of solving for x. The solution involves using logarithms and the laws of logarithms to simplify the problem. The conversation ends with a correction of a previous mistake made in the solution.
  • #1
EternityMech
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Hardest Math Problem EVAR!

Homework Statement



300 * 1,05x = 160 * 1.07x

Homework Equations



what is x?


The Attempt at a Solution



140 = 1,05x / 1.07x

i can solve this using a graphic calculator but i want to do it mathematically.
 
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  • #2


Your combined form should be 300/140=1.07^x/1.05^x. Take the log (any base) of both sides. Do you see how the laws of logarithms log(a*b)=log(a)+lob(b) and log(a^x)=x*log(a) can make this the easiest linear equation EVAR!
 
Last edited:
  • #3


is it 300/140 or 300/160?

thanks for the help.
 
  • #4


EternityMech said:
is it 300/140 or 300/160?

thanks for the help.

300/160, of course. Sorry about the slip.
 
  • #5


Edit: I mistook your post for being the solution to the problem
 
  • #6


(1.05/1.07)x = 160 / 300

got it muchos gracias.
 

FAQ: Solving for X: A Challenging Math Problem with Exponential Growth Rates

What is the concept of exponential growth?

Exponential growth is a mathematical concept where a quantity increases at a constant rate over time. This means that the amount by which the quantity increases also grows over time, leading to a rapid growth pattern.

How do you solve for X in a math problem with exponential growth rates?

To solve for X in a math problem with exponential growth rates, you need to use logarithms. By taking the logarithm of both sides of the equation, you can isolate X and solve for its value.

What are some real-life examples of exponential growth?

Some real-life examples of exponential growth include population growth, compound interest, and the spread of infectious diseases. In these scenarios, the quantity increases at a constant rate, leading to rapid growth over time.

Why is solving for X in a math problem with exponential growth rates important?

Solving for X in a math problem with exponential growth rates allows us to make predictions and understand the behavior of the quantity over time. It also helps us to analyze and make decisions based on the data that follows an exponential growth pattern.

What are some strategies for solving challenging math problems with exponential growth rates?

Some strategies for solving challenging math problems with exponential growth rates include using logarithms, graphing the data, and breaking down the problem into smaller, more manageable steps. It is also helpful to understand the properties of exponential functions and how they behave. Practice and patience are also key in solving these types of problems.

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