log2^2x-log2x-2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
W|-------------| W|-------------, -1|
\ 2 / \ 2 /
- ---------------- - --------------------
2 2
log (2) log (2)
−log(2)2W(−2e2log(2)2)−log(2)2W−1(−2e2log(2)2)
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
W|-------------| W|-------------, -1|
\ 2 / \ 2 /
- ---------------- - --------------------
2 2
log (2) log (2)
−log(2)2W(−2e2log(2)2)−log(2)2W−1(−2e2log(2)2)
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
-W|-------------| -W|-------------, -1|
\ 2 / \ 2 /
------------------*----------------------
2 2
log (2) log (2)
−log(2)2W(−2e2log(2)2)−log(2)2W−1(−2e2log(2)2)
/ 2 -2 \ / 2 -2 \
|-log (2)*e | |-log (2)*e |
W|-------------|*W|-------------, -1|
\ 2 / \ 2 /
-------------------------------------
4
log (2)
log(2)4W(−2e2log(2)2)W−1(−2e2log(2)2)
LambertW(-log(2)^2*exp(-2)/2)*LambertW(-log(2)^2*exp(-2)/2, -1)/log(2)^4
/ 2 -2 \
|-log (2)*e |
-W|-------------|
\ 2 /
x1 = ------------------
2
log (2)
x1=−log(2)2W(−2e2log(2)2)
/ 2 -2 \
|-log (2)*e |
-W|-------------, -1|
\ 2 /
x2 = ----------------------
2
log (2)
x2=−log(2)2W−1(−2e2log(2)2)
x2 = -LambertW(-exp(-2)*log(2^2/2, -1)/log(2)^2)