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kotovadasha08
@kotovadasha08
August 2022
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решите графически уравнение
[tex]log _{2}x= -x+1 [/tex]
[tex]log_{1/3}x = 2x-2[/tex]
[tex]x+2 = log _{8} x[/tex]
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avolkov777
1)log2x+x=1
log2x+log2x/log2x=1
log2^2x+log2x/log2x=1
log2x=log2^2x+log2x
log2^2x=0
x=1
2)-log3x/2=x-1
-log3x/log39=-log9x
-log9x-x=-1
log9x+x=1
log9^2x+log9x/log9x=1
log9^2x=0
x=1
3) все делаем также как и в первом уравнении и получаем
log8^2x-log8x=2log8x
log8^2x-3log8x=0
пусть log8x=t
t^2-3t=0
t1=0; t2=3
log8x=0
x=1
lpg8x=3
x=8^3=512
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Answers & Comments
log2x+log2x/log2x=1
log2^2x+log2x/log2x=1
log2x=log2^2x+log2x
log2^2x=0
x=1
2)-log3x/2=x-1
-log3x/log39=-log9x
-log9x-x=-1
log9x+x=1
log9^2x+log9x/log9x=1
log9^2x=0
x=1
3) все делаем также как и в первом уравнении и получаем
log8^2x-log8x=2log8x
log8^2x-3log8x=0
пусть log8x=t
t^2-3t=0
t1=0; t2=3
log8x=0
x=1
lpg8x=3
x=8^3=512