Can They Crack THIS Logarithmic Equation? Math Olympiad Challenge

Can They Crack THIS Logarithmic Equation? Math Olympiad Challenge

In this video, we're taking on the math Olympiad challenge: can they crack the logarithmic equation? Watch as we work our way through the equations!
The math Olympiad challenge is a fun way to challenge your brain and test your skills in mathematics. In this video, we're taking on the logarithmic equation, one of the more challenging puzzles in the math Olympiad. Can you help us solve the puzzle before time runs out?

Topic Covered:
1) Logarithmic equations
2) Math Olympiad
3) Logarithm problems
4) Math competition
5) Logarithm techniques
6) Math tutorial
7) Advanced math
8) Problem-solving
#logarithms #matholympiad #mathcompetition #mathtutorial #problemsolving #advancedmaths #MathSkills #mathematics

7 Key moments of this Video:
0:00 Introduction
0:37 Natural log
0:59 Properties of logarithm
1:28 Substitution
2:34 Factorization
3:00 Finding solutions
4:10 Verify results

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Thanks for watching video!!
@infyGyan ​

[borisfilipovic]

Another way:
1. Squere all:
logx*logx/4=logx
2. Devide
logx=4
3. by base of 10
x=10exp4

[اممدنحمظ]

تمرين جميل جيد . شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا. تحياتنا لكم من غزة فلسطين .

[mokouf]

I made a careless mistake which made the non-zero solution being x = 10^(1/4)
We REALLY need to use u-sub (okay, you use t instead) to avoid this!

[walterwen]

Math Olympiad Challenge: log√x = √(logx); x = ?
log√x = (1/2)logx = √(logx), [(1/2)logx]^2 = 1/4(logx)^2 = logx,
(logx)^2 – 4logx = (logx)(logx – 4) = 0, logx = 0 or logx – 4 = 0
logx = log(10^0) = 0; x = 10^0 = 1 or logx = log(10^4) = 4; x = 10^4
Answer check:
x = 1, log√x = log√(10^0) = 0 = √log(10^0) = √(logx); Confirmed
x = 10^4, log√(10^4) = 2, √(logx) = √(log10^4) = √4 = 2; Confirmed
Final answer:
x = 1 or x = 10^4