Why so complicated? It‘s way faster and much less error-likely to start with 4^x=2^(2x)=24=2^3*3 (line1) Then take log_2 on each side gives 2x=3+log_2(3) (line2) Immediately turns into x=3/2+log_2(3)/2 *done* Note: just writing „log“ without any base is wrong Notation! Either be specific and note log_b or use defined abbreviations like ln, lg, lb but not log.
Watch 110+ most important olympiad questions with solutions by just clicking on the link below th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
You don’t even need to show the division of logs on the left hand side. Just do a log with base “4” on both sides. That just leaves “X” on the left hand side and immediately leaves log 24/log4 on the right. It’s stupid to constantly show the division of logs when the equation a^log b base a=b is far faster.
Perché complicarsi la vita? Per definizione di logaritmo si trova immediatamente x = log4(24) = log4(4*6) = log4(4)+log4(6) = 1 + log4(6). Cambiando la base avremo x = 1 + ln6/ln4 oppure (log decimale), x = 1 + log6/log4
Watch 110+ most important olympiad questions with solutions by just clicking on the link below th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Watch 110+ most important olympiad questions with solutions by just clicking on the link below th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Watch 110+ most important olympiad questions with solutions by just clicking on the link below th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Watch 110+ most important olympiad questions with solutions by just clicking on the link below th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Watch 110+ most important olympiad questions with solutions by just clicking on the link below th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Stanford University entrance exam: 4ˣ = 24; x =? log4ˣ = log24 = log(4)(6), x = log₄4 + log₄(2)(3) = 1 + 1/2 + log₄3 = 1.5 + 0.793 = 2.293 The calculation was achieved on a smartphone with a standard calculator app Answer check: x = log₄24 = 2.293: 4ˣ = 4^(log₄24) = 24; Confirmed Final answer: x = log₄24 = 2.293
Watch 110+ most important olympiad questions with solutions by just clicking on the link below th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Why so complicated?
It‘s way faster and much less error-likely to start with 4^x=2^(2x)=24=2^3*3 (line1)
Then take log_2 on each side gives 2x=3+log_2(3) (line2)
Immediately turns into x=3/2+log_2(3)/2 *done*
Note: just writing „log“ without any base is wrong Notation! Either be specific and note log_b or use defined abbreviations like ln, lg, lb but not log.
thank you so much for sharing short method
Watch 110+ most important olympiad questions with solutions by just clicking on the link below
th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html
Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
You don’t even need to show the division of logs on the left hand side. Just do a log with base “4” on both sides. That just leaves “X” on the left hand side and immediately leaves log 24/log4 on the right. It’s stupid to constantly show the division of logs when the equation a^log b base a=b is far faster.
Perché complicarsi la vita? Per definizione di logaritmo si trova immediatamente x = log4(24) = log4(4*6) = log4(4)+log4(6) = 1 + log4(6). Cambiando la base avremo x = 1 + ln6/ln4 oppure (log decimale), x = 1 + log6/log4
Nice job, thanks
Watch 110+ most important olympiad questions with solutions by just clicking on the link below
th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html
Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
4ⁿ=24
(2²)ⁿ=2³3
2²ⁿ=2³3
2²ⁿ-³=3
log2²ⁿ-³=log3
(2n-3)log2=log3
2n-3=log3/log2
2n-3≈0,477/0,301
2n-3≈477/301
2n-3≈1+(176/301)
2n≈4+(176/301)
n≈2+(88/301)
n≈2+0,292
n≈2,292
Awesome dear, thanks
Watch 110+ most important olympiad questions with solutions by just clicking on the link below
th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html
Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Divide by 8
2^(2x-3) = 24/8
(2x-3) lg 2 = lg 3
2x - 3 = (lg 3 / lg 2)
2x = 3 + (lg 3 / lg 2)
x = (3 + (lg 3 / lg 2)) / 2
Great job, thanks
Watch 110+ most important olympiad questions with solutions by just clicking on the link below
th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html
Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
x=log24/log4=(log4/log6)/log4≈(0.602+0.778)/0.602≈1.38/0.778≈2.2924.
Deviation is about 0.0001.
ok
Bro i would do 24/4 😭
why?
Watch 110+ most important olympiad questions with solutions by just clicking on the link below
th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html
Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
4^x = 24
x lg(4) = lg(24)
x = lg(24)/lg(4)
x = (3 lg(2) + lg(3)) / (2 lg(2))
x = 1 + lg(6)/lg(4)
x = 1 + log₄6
Great job dear, thanks
Watch 110+ most important olympiad questions with solutions by just clicking on the link below
th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html
Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!
Stanford University entrance exam: 4ˣ = 24; x =?
log4ˣ = log24 = log(4)(6), x = log₄4 + log₄(2)(3) = 1 + 1/2 + log₄3 = 1.5 + 0.793 = 2.293
The calculation was achieved on a smartphone with a standard calculator app
Answer check:
x = log₄24 = 2.293: 4ˣ = 4^(log₄24) = 24; Confirmed
Final answer:
x = log₄24 = 2.293
beautiful explanation, thanks
Watch 110+ most important olympiad questions with solutions by just clicking on the link below
th-cam.com/play/PLybCHBiqtqWP-TrcsG21MXXxlknROi514.html
Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!