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25x = 250 x = log 250 / log 25 x = 1.71534 25^1.71534 = 250

x=log250/log25=(log25+log10)/log25=1+1/2log5 x≈1+1/(2×0.699)≈1199/699≈1.71532 Deviation is about 0.00003 25^1.71532≈249.985

x=log180/log6=(2log6+log5)/log6=2+log5/(log2+log3) x≈2+0.699/(0.301+0.477)≈2255/778≈2.898 Deviation is about 0.0002 6^2.898≈179.92

You can simplify it further by doing: 4^x = 16 * 3 Taking log base 4 on both sides, x = log4(16*3) x=log4(16) + log4(3) x=2+log4(3) You can do it with the answer you found aswell by seeing that 1+log4(12) = 1+log4(4*3) = 1+log4(4)+log4(3) = 2+log4(3)

GOODBYE

I think you should have explained in more detail the following: 5*√3*i × (-5)*√3*i = (-25)*(+3)*(-1) = (-75)*(-1) = +75 ✓

x=2?

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x=log50/2log5=(log5+log10)/2log5≈(0.7+1)/(2×0.7)≈17/14≈1.214. Deviation is about 0.001.

Mai class 10 ke student ho fbise board sai and Menai thumnail daikh kr question solve kiya and ans check krnai kai liai ap ke video daikhe or mera answer sai hai. yai tricky problem hai? 🤔9th and 10th ke math per yai concept he to pera hai.

15×256²=983040.

x=log15/log3=(log3+log5)/log3≈(0.48+0.7)/0.48≈59/24≈2.4583. Deviation of only 0.0066.

Firstly, you should not write "log" without giving any base. Many people write "log()" intending base 10 (Caution: other people intend base e then, which is "ln()" !), but they should write "log_10_()" or just "lg()" instead. Secondly, it is more straightforward to use the base 4 for the logarithm, as the exponential equation has base 4, too: 4^x = 48 x = log_4_(48) x = 2.79248... In this form, you can type in into many modern calculators to get the numerical value of the solution x. However, if you want to simplify this, you can write = log_4_(16 * 3) = log_4_(16) + log_4_(3) = log_4_(4^2) + log_4_(3) = 2 + log_4_(3) If you want to transform it to base 10, which I write lg(), you can use the base converting rule: log_4_(...) = lg(...) / lg(4) In this case x = 2 + log_4_(3) = 2 + lg(3)/lg(4) which is equal to = 1 + log_4_(12) given in the video. Instead of lg(), you can also use ln() in the numerator and denominator of these fractions. It doesn't really matter which base you use. The reason for using lg or ln is that many older or weaker calculators offer only one type of logarithm to a fixed base, namely 10 or e. But as I said, better calculators usually offer a general "log" key, which allows to set an arbitrary (positive) base, like 4 in this case, so you don't need the base converting rule anymore.

x=log48/log4=(log6+log8)/log4≈(0,78+0,9)/0,6≈1,68/0,6≈14/5. Absulute error is about 0,0075.

x^2/36=36/x^2 => x^2/36 = 1/ x^2/36 /*(x^2/36) => x^4/36^2 = 1 => x^4=36^2 => x^2=36 => x=6

Oh😢

As x^2/36=x^2/36 X^2/x^2= 36/36 X^4 = 1296 (36x36) X = 4√1296 = 144

X is 144

This in an exercise on how to make a simple sum complicated! Consider 8^8=(((8^2)^2)^2=(64^2)^2=4,096^2=16,777,216. So 8^8-88=16,777,128. The multiplication involved is trivial.

Hello? I have used your thumbnail a little bit. Would you mind if I ask could you see my solution way please? :)

16^5 - 16^4 = 16^4 ( 16 - 1 ) 16 ^4 (15)

Japanese Math Olympiad Question: √(x + 2) + √(x - 4) = 6; x =? 6 > √(x + 2) > √(x - 4) > 0; Let: y = x - 1, x + 2 = y + 3, x - 4 = y - 3 √(x + 2) + √(x - 4) = √(y + 3) + √(y - 3) = 6, [√(y + 3) + √(y - 3)]² = 6² (y + 3) + 2√[(y + 3)(y - 3)] + (y - 3) = 36, √(y² - 9) = 18 - y, y² - 9 = (18 - y)² y² - 9 = y² - 36y + 18², 36y = 18² + 9, y = [9(36 + 1)]/36 = 37/4 = x - 1, x = 41/4 Answer check: √(x + 2) + √(x - 4) = 6 x = 41/4: √(41/4 + 2) + √(41/4 - 4) = √(49/4) + √(25/4) = 7/2 + 5/2 = 6; Confirmed Final answer: x = 41/4 = 10.25

What was the shortcut promise in description of video?

(15)16^4 = (15) 2^16 = (15)(1024)(64) = (30)(512)(64) = (15360)(60+4) = 921600+61440 = 983040

much easier way is not this way.

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If everyone at the Olympics were as fast as you, the world record for 100 meters would be at 3 h 15 min and 29 sec.

x^4 = 4^4 x^2 = +/- 16 x = +/- 4, +/- 4i

Man, you just do complex 4th root from 4^4 ... that is a one-liner...

SIR SIR SIR SIR HELLO SIT

5^(х-2)=5^2 X-2=2 X=4

Cut the BS. Factor 4^x out without using the fancy 2-1

1) Factor out √5 top and bottom and cancel leaving (√6+1)/(√6-1) 2) Rationalize the denominator

Since the cube of m is bigger than its square when |m| > 1, a real root will be where |m|^3 is a bit less than 150. That suggests |m| = 5. Then m^2 - m^3 = 25 - (-125) = 150, making m = -5. We can now factorise m^3 - m^2 + 150 = 0 because (m + 5) is a factor. So let (m + 5)(m^2 + Am + 30) be the factorisation, then we can see that A = -6 makes the coefficient of m equal to 0. Solve m^2 - 6m + 30 with the quadratic formula x = -(b/2) ± √( (b/2)^2 - ac) = 3 ± √(9 - 30) = 3 ± i√21

brilliant video g

Answering without watching the video Quite a simple question with a little trick to it. Took less tha a min to solve with pure metal calculation Ans: -5

at 1:39 you can't put a bracket with a minus outside without multiplying the terms inside with -1

you fail to prove that 5*(log2/log5)=2

Your solution is wrong the log won't be used separately for the lhs the whole term will be under a single log function

Die Mathematik (bundesdeutsches Hochdeutsch: [matemaˈtiːk], [matemaˈtik]; österreichisches Hochdeutsch: [mateˈmaːtik];[1] von altgriechisch μαθηματικὴ τέχνη mathēmatikē téchnē ‚die Kunst des Lernens‘) ist eine Formalwissenschaft, die aus der Untersuchung von geometrischen Figuren und dem Rechnen mit Zahlen entstand. Für Mathematik gibt es keine allgemein anerkannte Definition; heute wird sie üblicherweise als eine Wissenschaft beschrieben, die durch logische Definitionen selbstgeschaffene abstrakte Strukturen mittels der Logik auf ihre Eigenschaften und Muster untersucht. Reutersvärd-Dreieck, das im Kern eine Segmentierung des Penrose-Dreiecks ist, als Veranschaulichung für unmögliche Figuren, die eine Schnittstelle zwischen Kunst und Mathematik darstellen0:14

Seriously?

Haha, so, now, 1 = 2 Illogical

Germany Math Olympiad Problem: (3ˣ)(3ˣ)(3ˣ) = 21; x =? (3ˣ)(3ˣ)(3ˣ) = 3³ˣ = 21, 3x = log₃21 = log₃3 + log₃7 = 1 + 1.771, x = 2.771/3 = 0.924 The calculation was achieved on a smartphone with a standard calculator app Answer check: x = 0.924, 3x = log₃21: (3ˣ)(3ˣ)(3ˣ) = 3³ˣ = 3^log₃21 = 21; Confirmed Final answer: x = (log₃21)/3 = 0.924

Calculation lengthy and confusing.

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Tnx bro😊😊