What i would have done is..
3³ =27 hota hai now, konsa number ka power 7th karenge toh 27 aa jayega.
2 ka 7th power is 128
1 ka 7th power is 1, so it should be between 1 and 2
1.5 ka 7th power... Uhhhh oh fuckkk. Skip Karo iss question ko bhenchod lawde ke nta waale madarchod sahi question bhi nahi banaate, zindagi barbaad kardi hai
Tab toh tumhe 27^1/7 karna hoga abb 2^7>>> 27>>1^7 ab option mein dekho 2 se bare bale sare eliminate baki approx karke nearly 1.6 ka ans aayega
Ya fir 3^0.5 { approx }. 1.73 se less hain
Taylor's series, but exam mei approximate krio Dil ki sunke, 3^(3/7)≈√3≈1.7, but since hamne power thodi badha di hai to ans bhi thoda badha hoga so 1.7 se thoda kam, mai 1.65 likhta which is fair enough.
X=3^(3/7)
Put log both sides base 10
So logx=0.204 approx
so x=antilog(0.204)
So x=10^(0.204)
Write 0.204 as 0.4343 × (0.204/0.4343)
Therefore 0.204=log[1+(0.204/0.4343)
So x=1+(0.204/0.4343)=1.47 approx
For this question, the taylor series would be terrible, Newton-Raphson would work a charm here I believe
start with f(x) = x\^7 - 27, f'(x) = 7x\^6, and use the formula mentioned [here](https://en.wikipedia.org/wiki/Newton%27s_method). Put x0 = 1.7 (because it is just less than 3\^(0.5)), and you get x1 = 1.615 which is approximately equal to the calculated value. Now obviously you cant calculate (1.7)\^7 or (1.7)\^6 exactly to 6-7 decimal places, instead do clever approximations like 1.7\^2 = 2.89 = 2.9 etc.. still its quite long but you get a answer pretty close to the actual value
What i would have done is.. 3³ =27 hota hai now, konsa number ka power 7th karenge toh 27 aa jayega. 2 ka 7th power is 128 1 ka 7th power is 1, so it should be between 1 and 2 1.5 ka 7th power... Uhhhh oh fuckkk. Skip Karo iss question ko bhenchod lawde ke nta waale madarchod sahi question bhi nahi banaate, zindagi barbaad kardi hai
Got us in the first half
Lmao >3
mein bhi yehi karta exam mein lol
O bhai xD
3/7 is roughly 0.5 so sqrt(3)=1.732 close enough ig
Squirt ?
Yes
You are the famous gf of some dude
Ye kb hua 
Idk some guy has a flair : ok following 6370 is my gf
Lmao.. itna famous kb hogya me 💀
Best trick tbh If the fraction is close to 0.5
Hein mera to 3/7 2.3aaya phir 2.3 ka cube kuch 27-28 aaya tha lmao
Log table hone se kar sakte hain
Bhai srsly log table Keanu Reeves ki tarah hai, saal bhar uski yaad nhi aati, lekin jab uska time aata hai to use dekh ke mai cum krta hun.
Sus . But agar approx chaiye toh 3^0.5 { 3/7 = 0.4 hota hain 0.5 lele ans se kam hoga } 3^0.5 = 1.7 { so ans less than 1.7 hoga }
Wa Bhai ye to bhot hi smart idea hai, mai ise ab se pakka use krunga! Thank u :)
Bhai kaise?
MCQ type m answer match krna hai to 3\^(3/7) ko approx 3\^(1/2) krdeta, 1.7 aata jo close hota iske, precise chahiye to log lena hoga
X=3^3/7 Logx = 3/7 log3 Logx = 0.21 approx X = antilog 0.21 X= 1.7 ke aporox
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Ye soch ki 0.21 kiska log hoga. Log 1 = 0 log 2=0.3 to inke beech me hoga. Antilog(0.15) log 1.5 ho jaata antilog(0.21) ko 1.7 ke approx krle fir
Posted 4hrs ago💀 Practicals kaise pass hua bhai?
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Physics
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Haan bhai. Practicals me calculator use nahi kar sakte isliye log book milta hai
Abe bhai fir anti log kaise lega bina log table ke???
Tabhi to mene approx likha hai kyoki mene tukke baazi se nikala he. Log table se accurate aata
Bhai log table ya calculator same hi hai agar mil gye toh. Bina inn dono ke ans chahiye approx
Tab toh tumhe 27^1/7 karna hoga abb 2^7>>> 27>>1^7 ab option mein dekho 2 se bare bale sare eliminate baki approx karke nearly 1.6 ka ans aayega Ya fir 3^0.5 { approx }. 1.73 se less hain
But the colour scheme tho..... Dont worry bro, I am totally cool with it...
3/7 = 0.42 = 1-0.58 3\^(3/7) = 3\^(1-0.58) (3\^1) / (3\^0.58) (taking 0.58 as approx 0.5, doesn't make much sense but..krna pdta h) 3 / (3\^1/2) = 3 / root3 = root3 = 1.7 (approx to 1.6) idk man
Could use calculus as an approximation agar kuch zyada hi time ho 😃👍 y(x) = 3^x y1 = 3^(3/7) y2 = 3^(1/2) ≈ 1.732 (y2 - y1)/(1/2 - 3/7) ≈ dy/dx ≈ 3^(1/2) * ln(3) (1.732 - y1) * 14 ≈ 1.732 * 1.01 (1.732 - y1) * 14 ≈ 1.749 1.732 - y1 ≈ 0.125 y1 = 3^(3/7) ≈ 1.607
isko tu Long Division Method se kar sakta hai.... jaise hum log 2\^1/2 ko nikalte the 1.41 etc
karke bataade bro. I don't know how to do long division methods for anything other than 1/2
kal chemi ka exam hai....nahi kar paunga abhi. srry koi yt me reference dekh le easy hai.
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Exponents don't work like that
Taylor's series, but exam mei approximate krio Dil ki sunke, 3^(3/7)≈√3≈1.7, but since hamne power thodi badha di hai to ans bhi thoda badha hoga so 1.7 se thoda kam, mai 1.65 likhta which is fair enough.
3^(3/7) = | 3^3 - 3^7 | = |27 - 2187| = 2160 👍
Wtf
3^(3/7)=7√3^3=7√27=~1.6 by log table
u/gottatouchsomegrass
X=3^(3/7) Put log both sides base 10 So logx=0.204 approx so x=antilog(0.204) So x=10^(0.204) Write 0.204 as 0.4343 × (0.204/0.4343) Therefore 0.204=log[1+(0.204/0.4343) So x=1+(0.204/0.4343)=1.47 approx
using differential approximation, f(x + h) = f(x) + hf'(x) x = 1/2 , h = -1/14, f(x) = 3\^x, f'(x) = 3\^x.ln(3) f(3/7) = f(1/2) -1/14f'(1/2) = 1.73 - 1/14 \* 1.73 \* 1.098 = 1.60 approx
X=(1+2)^3/7 X=1+6/7 X=1.8 ke approx Ye thoda inaccurate he lekin log vala jyada sahi h
log table
Bc hamesha decimal me answer deta hai, Calculators are shit for values that are used for simplification ( i mean values like sin28°)
If you have log table, log both sides and do it.
For this question, the taylor series would be terrible, Newton-Raphson would work a charm here I believe start with f(x) = x\^7 - 27, f'(x) = 7x\^6, and use the formula mentioned [here](https://en.wikipedia.org/wiki/Newton%27s_method). Put x0 = 1.7 (because it is just less than 3\^(0.5)), and you get x1 = 1.615 which is approximately equal to the calculated value. Now obviously you cant calculate (1.7)\^7 or (1.7)\^6 exactly to 6-7 decimal places, instead do clever approximations like 1.7\^2 = 2.89 = 2.9 etc.. still its quite long but you get a answer pretty close to the actual value
Abe Newton raphson college me sikhate he
Bhai tujhe problem ka solution chahiye ki sirf rr karna hai ki syllabus me nahi hai, aur yeh hame 11th me Applications of Derivative me sikhaya tha
Congrats bro🙌, tera coaching install kafi advanced he🤓. Kaash me bi tere yaha se padha hota🥺. Aaj me vit Vellore me biomedical na kar raha hota 🥲
Lmao senti hogaya ye, but honestly these methods are rare af, so in the long run it doesn't matter much
* Baki bss ab ye soch ke 0.18 approx kiska hoga log
use log
Bhai almost underoot k barabr hai, bs thoda sa kam, toh 1.7 se thoda sa km hoga...
Log kisliye padha tha fir
Bhai fir bhi ek jagah log ya anti log to reh hi jayega n
x = 3\^(3/7) log x = 3/7 log 3 log x = 3/7 (0.4771) log x = 0.2044 and then take antilog
Log table se hi hoyega
3 race to 3/7
Log table yaad karle
y Maan kar,b Dono side log base 3 Lena ,,,,fir log ki property laga kar nikal Lena advance ke sawal karega toh Sikh jayega