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

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The equation 4^x = 8x presents challenges for algebraic solutions due to its transcendental nature. While taking the natural logarithm was attempted, it did not yield helpful results. The equation has two real solutions, which can be determined graphically. Additionally, the solutions can be expressed using the Lambert W function. Understanding these methods is essential for solving such equations effectively.
amcavoy
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Wow, I can't believe I couldn't do this.

4^x=8x

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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who says you can do it algebraically?
 
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.
 
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Alright well thanks for your help.
 

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