How Do You Solve Exponential Equations Using Logarithms?

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Homework Help Overview

The problem involves solving an exponential equation of the form 12^x = 4 × 8^(2x), with participants discussing the application of logarithms to simplify and solve the equation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest using logarithms to simplify both sides of the equation. There are attempts to clarify the application of logarithmic rules, such as log(a*b) = log(a) + log(b) and log(a^b) = b*log(a). Some participants express confusion about the initial steps and seek further explanation.

Discussion Status

The discussion is ongoing, with some participants providing guidance on using logarithms while others express difficulty in understanding the simplification process. There is no explicit consensus, but a direction towards using logarithmic properties is evident.

Contextual Notes

Participants are navigating the complexities of logarithmic rules and their application to the given exponential equation, indicating a need for clarification on foundational concepts.

moe11
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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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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?
 


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.
 


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).
 


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).
 

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