Crushing Exponential Equations: Log Tactics for Math Olympiad Victory!

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Crushing Exponential Equations: Log Tactics for Math Olympiad Victory!
Get ready to elevate your Math Olympiad game to new heights with our in-depth exploration of crushing exponential equations using logarithmic tactics! In this video, we'll unravel the complexities of exponential equations and reveal powerful logarithmic strategies that will lead you to victory in Math Olympiad competitions. Whether you're a seasoned competitor or just starting out, join us on this exhilarating journey as we arm you with the tools and techniques to conquer even the most challenging exponential equations. Don't miss your chance to master the art of logarithmic tactics and seize the glory in Math Olympiad!
Topics covered:
Exponential equations
How to solve exponential equations?
Logarithms
Properties of logarithm
Algebra
Properties of exponents
Algebraic identities
Factorization
Exponential Equation
Logarithms
Math Olympiad preparation
Math Olympiad training
Exponent laws
Solving quartic equation
Quadratic equation
Complex solutions
Real solutions
Timestamps:
0:00 Introduction
0:24 Properties of logarithm
3:52 Solving Quartic equation with factorization
6:50 Algebraic identities
8:20 Quadratic equation
9:20 Quadratic formula
9:57 Solutions
10:32 Verification
#matholympiad #exponentialequations #logarithms #problemsolving #mathematics #competitiontips #victorystrategies #mathletes #stemeducation #solvingequations #olympiadpreparation
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infyGyan

[@mohammedsaysrashid3587]

Thanks for sharing.....it was a wonderful explanation....x=4

[@user-kp2rd5qv8g]

log_4 (x) = t > t^4-4t+3=0 > t -1 is the only real solution. Therefore, x=4.

[@tunneloflight]

That there is a log base 4 suggests that x is likely a multiple of 4. Testing 4, since log4(4) =1 results in x^(1^3) = 4. 4^4/64 = 4. so 4 = 4. check. We know x>0, as 0 to any power is invalid, and logarithms of negative numbers are undefined. For x less than 1, the value of the LHS increases with decreasing x, beginning at 1 and rising, while the right hand side starts at 1/64 and declines. So x >1. For X greater than 1, both LHS and RHS are smoothly rising. The RHS starts lower and rises faster than the LHS, so there is only one solution. X = 4.

[@tunneloflight]

Or - you can go through the exercise of converting everything to log base 4. and end up solving (log4(x))^4 - 4*log4(x) +3 = 0. But again, the obvious solution to that is x = 4, hence 1^4 - 4 +3 = 0. The other three roots are negative and two imaginary roots. So only x. =4.