Logarithms homework question

In summary, The conversation is about solving the equation 12^x=4X8^(2x) and using logarithms to simplify it. The person asking for help is having trouble understanding how to use logarithms and asks for an explanation. The expert reminds them of the logarithm rules and suggests taking the log of both sides to simplify the equation.
  • #1
moe11
8
0

Homework Statement


12^x=4X8^(2x)

Big X= multiplication sign
little x= unknown

i simply cannot figure this out. Any help please?

Homework Equations


4.6X1.06^(2x+3)=5X3^(x)
 
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  • #2


Use logarithms! Isn't that your title? Take the log of both sides and use the rules of logarithms to simplify. What do you get?
 
  • #3


Dick said:
Use logarithms! Isn't that your title? Take the log of both sides and use the rules of logarithms to simplify. What do you get?

i wouldn't post this if i could do it as easily as you said. Can you explain? Thats why I'm here.
 
  • #4


log(12^x)=log(4*8^(2x)). That wasn't so hard. Now simplify it. Use rules of logarithms like, log(a*b)=log(a)+log(b), log(a^b)=b*log(a).
 
  • #5


Your equation is 12x=(4)82x.

Since you titled this "logarithms", Dick assumed you knew some basic rules of logarithms. Take the logarithm of both sides: log(12x= log((4)82x)

Now use the fact that log(ab)= log(a)+ log(b) and that log(ax)= x log(a).
 

What are logarithms and why are they important?

Logarithms are mathematical functions that represent the inverse of exponentiation. They are used to solve exponential equations and to make large numbers more manageable. They are important in various fields of science, such as chemistry, physics, and biology, as well as in finance and engineering.

How do I solve logarithm equations?

To solve a logarithm equation, you can use the properties of logarithms, such as the product, quotient, and power rules. You can also convert logarithms into exponential form and vice versa. It is important to note the base of the logarithm when solving an equation, as it will affect the solution.

What are common mistakes to avoid when working with logarithms?

Common mistakes when working with logarithms include forgetting to apply the appropriate logarithm rule, mixing up the base of the logarithm, and making errors when simplifying logarithmic expressions. It is important to double check your work and be familiar with the properties of logarithms.

What real-life applications use logarithms?

Logarithms have many real-life applications, such as in earthquake magnitude scales, pH levels in chemistry, decibel levels in sound, and the Richter scale for measuring the intensity of earthquakes. They are also used in financial calculations, such as compound interest and population growth.

How can I improve my understanding of logarithms?

To improve your understanding of logarithms, practice solving various logarithm equations, work on real-life application problems, and review the properties of logarithms. You can also seek help from a tutor or attend a workshop to strengthen your knowledge and skills in working with logarithms.

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