A Nice Algebra Problem | Math Olympiad | A Tricky Exponential Equation

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Find the value of x?
How to solve 4^x = 24

In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation 4^x = 24 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra

[ECUC_Studioz]

If doing the other stuff is not necessary, then using log to base 4 would have minimized the steps needed to solve the equation as log properties mean applying log to the appropriate base on both sides of the equation means on one side, the base and its respective log would cancel out, leaving whatever is on the exponent as another log property already drops the exponent to the front of the log and multiplied. In this case, log to base 4 will result in solving the equation with minimal steps assuming log of 24 to base 4 is it without doing anything else.

[geirs]

Rewrite as
2^(2x) = (2^3) * 3
Divide by 2^3 and get
2^(2x - 3) =3
Take ln of each side and solve for x
x = 3/2 + 1/2 * ln3/ln2

[subratabiswas]

x=log24/log4 ; i, e x= (3log2+log3)/2log2 ; i, e x= (3/2)+(1/2).(log3/log2).

[Ronaldocr-ph]

4^x=24
log(4^x)=log(24)
x×log(4)=log(24)
x=log(24)÷log(4)
x=2.29248125...