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.
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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
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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
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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
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
Bro i would do 24/4 😭
why?
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