1) (1-log5(40))(1-log8(40))
2) (1-log4(32))(1-log8(32))
пожалуйста, решите!
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Ответил alfabetta
0
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Ответил m11m
0
1)
![(1-log_{5}(5*8))(1-log_{8}(8*5))= \
=(1-(log_{5}5+log_{5}8))(1-(log_{8}8+log_{8}5))= \
=(1-1-log_{5}8)(1-1-log_{8}5)=-log_{5}8*(-log_{8}5)= \
=log_{5}8* frac{1}{log_{5}8}=1](https://tex.z-dn.net/?f=%281-log_%7B5%7D%285%2A8%29%29%281-log_%7B8%7D%288%2A5%29%29%3D+%5C+%0A%3D%281-%28log_%7B5%7D5%2Blog_%7B5%7D8%29%29%281-%28log_%7B8%7D8%2Blog_%7B8%7D5%29%29%3D+%5C+%0A%3D%281-1-log_%7B5%7D8%29%281-1-log_%7B8%7D5%29%3D-log_%7B5%7D8%2A%28-log_%7B8%7D5%29%3D+%5C+%0A%3Dlog_%7B5%7D8%2A+frac%7B1%7D%7Blog_%7B5%7D8%7D%3D1+ "(1-log_{5}(5*8))(1-log_{8}(8*5))= \
=(1-(log_{5}5+log_{5}8))(1-(log_{8}8+log_{8}5))= \
=(1-1-log_{5}8)(1-1-log_{8}5)=-log_{5}8*(-log_{8}5)= \
=log_{5}8* frac{1}{log_{5}8}=1")
2)
![(1-log_{4}(4*8))(1-log_{8}(8*4))= \
=(1-(log_{4}4+log_{4}8))(1-(log_{8}8+log_{8}4))= \
=(1-1-log_{4}8)(1-1-log_{8}4)=-log_{4}8*(-log_{8}4)= \
=log_{4}8* frac{1}{log_{4}8}=1](https://tex.z-dn.net/?f=%281-log_%7B4%7D%284%2A8%29%29%281-log_%7B8%7D%288%2A4%29%29%3D+%5C+%0A%3D%281-%28log_%7B4%7D4%2Blog_%7B4%7D8%29%29%281-%28log_%7B8%7D8%2Blog_%7B8%7D4%29%29%3D+%5C+%0A%3D%281-1-log_%7B4%7D8%29%281-1-log_%7B8%7D4%29%3D-log_%7B4%7D8%2A%28-log_%7B8%7D4%29%3D+%5C+%0A%3Dlog_%7B4%7D8%2A+frac%7B1%7D%7Blog_%7B4%7D8%7D%3D1+ "(1-log_{4}(4*8))(1-log_{8}(8*4))= \
=(1-(log_{4}4+log_{4}8))(1-(log_{8}8+log_{8}4))= \
=(1-1-log_{4}8)(1-1-log_{8}4)=-log_{4}8*(-log_{8}4)= \
=log_{4}8* frac{1}{log_{4}8}=1")
2)
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