How Do You Solve 4^x = 8x Algebraically?

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In summary, the equation "4^x=8x" means that 4 raised to the power of x is equal to 8 times x. To solve this equation, you can take the log of both sides and use algebraic manipulation and properties of logarithms. The answer to this equation is a range of values for x, as it has infinitely many solutions. This equation is important because it is a common type of exponential equation and can be used to model real-world situations such as population growth or radioactive decay.
  • #1
amcavoy
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Wow, I can't believe I couldn't do this.

[tex]4^x=8x[/tex]

I tried taking the natural logarithm of both sides, but that didn't help very much. I can see that an answer is 2, but I want to know how to get to that algebraicly.
 
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  • #2
who says you can do it algebraically?
 
  • #3
It has 2 real solutions which can be found graphically.The equation is transcendental.

The solutions are expressible in terms of the Lambert function

Daniel.
 
Last edited:
  • #4
Alright well thanks for your help.
 

FAQ: How Do You Solve 4^x = 8x Algebraically?

What does "4^x=8x" mean?

The equation "4^x=8x" means that the value of 4 raised to the power of x is equal to 8 times x. In other words, the value of 4 multiplied by itself x times is equal to 8 multiplied by x.

How do you solve "4^x=8x"?

To solve "4^x=8x", you can start by taking the log of both sides of the equation. This will help you isolate the variable x. After taking the log, you can use algebraic manipulation and properties of logarithms to solve for x.

What is the answer to "4^x=8x"?

The answer to "4^x=8x" is not a single number, but rather a range of values for x. This is because the equation has infinitely many solutions. The exact value of x depends on the context of the problem and the desired level of precision.

Why is "4^x=8x" important?

"4^x=8x" is important because it is a common type of exponential equation that appears in many scientific and mathematical problems. It also highlights the relationship between exponential and linear functions, and can be used to model real-world situations.

What are some real-world applications of "4^x=8x"?

One example of a real-world application of "4^x=8x" is in population growth models. The equation can also be used to calculate the half-life of a radioactive substance. In addition, it can be used to analyze the growth of bacteria in a lab setting or the spread of a virus in a population.

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