SOLUTION: Solve log(log x) + log(log x⁴ - 3) = 0

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Question 1139687: Solve log(log x) + log(log x⁴ - 3) = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28%28log+%28x%29%29%29+%2B+log%28%28log+%28x%5E4%29+-+3%29%29%29+=+0
Assuming "log" is the base 10.

log%28%28log+%28x%29%2A+log+%28x%5E4+-+3%29%29%29+=+0....since 0=log%2810%2C1%29,we have
log%28%28log+%28x%29%2A+%28log+%28x%5E4%29+-log%28+3%29%29%29%29+=+log%2810%2C1%29....simplify
log+%28%28x%29%29%2A+4%2Alog+%28%28x+-+3%29%29=1
Rewrite the equation with : log+%28%28+x+%29%29=u
u+%284u-3+%29=1
4u%5E2-3u=1
4u%5E2-3u-1=0
4u%5E2-4u%2Bu-1=0
%284u%5E2-4u%29%2B%28u-1%29=0
4u%28u-1%29%2B%28u-1%29=0
%284u%2B1%29%28u-1%29=0
=>u=1 or u=-1%2F4
then, find log+%28+10%2Cx+%29=u
=> when u=1
log+%28+10%2Cx+%29=1
x=10
=> when u=-1%2F4
log+%28+10%2Cx+%29=-1%2F4
x+=+10%5E%28-1%2F4%29%0D%0A%0D%0A%7B%7B%7Bx+=+1%2F10%5E%281%2F4%29
Check the solutions by plugging them into log%28%28log+%28x%29%29%29+%2B+log%28%28log+%28x%5E4%29+-+3%29%29+%29=+0
log%28%28log+%2810%29%29%29+%2B+log%28%28log+%2810%5E4%29+-+3%29%29%29+=+0........True
.... False
so, your solution is: x=10