Предмет: Алгебра,
автор: Akula17
308 полностью= 1 пример там
309-не надо
310-полностью – 1 пример там
311-не надо
312 – 2-ой пример .
313-не надо
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Ответы
Автор ответа:
0
308)
![log_{49}28=log_{7^2}28= frac{1}{2} log_{7}(4cdot7)= frac{1}{2}( log_{7}(4)+log_{7}(7))
\
= frac{1}{2}( log_{7}2^2+1)= frac{1}{2}( 2log_{7}2+1) =frac{1}{2}( 2m+1)=m+ frac{1}{2}](https://tex.z-dn.net/?f=log_%7B49%7D28%3Dlog_%7B7%5E2%7D28%3D+frac%7B1%7D%7B2%7D+log_%7B7%7D%284cdot7%29%3D+frac%7B1%7D%7B2%7D%28+log_%7B7%7D%284%29%2Blog_%7B7%7D%287%29%29%0A%5C%0A%3D+frac%7B1%7D%7B2%7D%28+log_%7B7%7D2%5E2%2B1%29%3D+frac%7B1%7D%7B2%7D%28+2log_%7B7%7D2%2B1%29+%3Dfrac%7B1%7D%7B2%7D%28+2m%2B1%29%3Dm%2B+frac%7B1%7D%7B2%7D+ "log_{49}28=log_{7^2}28= frac{1}{2} log_{7}(4cdot7)= frac{1}{2}( log_{7}(4)+log_{7}(7))
\
= frac{1}{2}( log_{7}2^2+1)= frac{1}{2}( 2log_{7}2+1) =frac{1}{2}( 2m+1)=m+ frac{1}{2}")
310)
![log_62=frac{1}{log_26}= frac{1}{log_2(3cdot2)}=frac{1}{log_23+log_22}=frac{1}{log_23+1}=m
\
Rightarrowlog_23=frac{1}{m}-1=frac{1-m}{m}
\\
log_{24}72=log_{24}(24cdot3)=log_{24}24+log_{24}3=1+ frac{1}{log_324}=
\
=1+ frac{1}{log_{3}(3cdot8)}=1+frac{1}{log_33+log_38}=1+frac{1}{1+log_32^3}=
\
=1+frac{1}{1+3log_32}=1+cfrac{1}{1+frac{3}{log_23} }](https://tex.z-dn.net/?f=log_62%3Dfrac%7B1%7D%7Blog_26%7D%3D+frac%7B1%7D%7Blog_2%283cdot2%29%7D%3Dfrac%7B1%7D%7Blog_23%2Blog_22%7D%3Dfrac%7B1%7D%7Blog_23%2B1%7D%3Dm%0A%5C%0ARightarrowlog_23%3Dfrac%7B1%7D%7Bm%7D-1%3Dfrac%7B1-m%7D%7Bm%7D%0A%5C%5C%0Alog_%7B24%7D72%3Dlog_%7B24%7D%2824cdot3%29%3Dlog_%7B24%7D24%2Blog_%7B24%7D3%3D1%2B+frac%7B1%7D%7Blog_324%7D%3D%0A%5C%0A%3D1%2B+frac%7B1%7D%7Blog_%7B3%7D%283cdot8%29%7D%3D1%2Bfrac%7B1%7D%7Blog_33%2Blog_38%7D%3D1%2Bfrac%7B1%7D%7B1%2Blog_32%5E3%7D%3D%0A%5C%0A%3D1%2Bfrac%7B1%7D%7B1%2B3log_32%7D%3D1%2Bcfrac%7B1%7D%7B1%2Bfrac%7B3%7D%7Blog_23%7D+%7D "log_62=frac{1}{log_26}= frac{1}{log_2(3cdot2)}=frac{1}{log_23+log_22}=frac{1}{log_23+1}=m
\
Rightarrowlog_23=frac{1}{m}-1=frac{1-m}{m}
\\
log_{24}72=log_{24}(24cdot3)=log_{24}24+log_{24}3=1+ frac{1}{log_324}=
\
=1+ frac{1}{log_{3}(3cdot8)}=1+frac{1}{log_33+log_38}=1+frac{1}{1+log_32^3}=
\
=1+frac{1}{1+3log_32}=1+cfrac{1}{1+frac{3}{log_23} }")
312)
![frac{log_2192}{log_{12}2} - frac{log_224}{log_{96}2} =
log_2192log_212 - log_224log_296 =
\
=log_2(3cdot2^6)log_2(3cdot2^2) - log_2(3cdot2^3)log_2(3cdot2^5) =
\
=(log_23+log_22^6)(log_23+log_22^2) - (log_23+log_22^3)(log_23+log_22^5)
\
=(log_23+6)(log_23+2) - (log_23+3)(log_23+5) =
\
=log_2^23+2log_23+6log_23+12-log_2^23-5log_23-3log_23-15=-3](https://tex.z-dn.net/?f=+frac%7Blog_2192%7D%7Blog_%7B12%7D2%7D+-+frac%7Blog_224%7D%7Blog_%7B96%7D2%7D+%3D%0Alog_2192log_212+-+log_224log_296+%3D%0A%5C%0A%3Dlog_2%283cdot2%5E6%29log_2%283cdot2%5E2%29+-+log_2%283cdot2%5E3%29log_2%283cdot2%5E5%29+%3D%0A%5C%0A%3D%28log_23%2Blog_22%5E6%29%28log_23%2Blog_22%5E2%29+-+%28log_23%2Blog_22%5E3%29%28log_23%2Blog_22%5E5%29+%0A%5C%0A%3D%28log_23%2B6%29%28log_23%2B2%29+-+%28log_23%2B3%29%28log_23%2B5%29+%3D%0A%5C%0A%3Dlog_2%5E23%2B2log_23%2B6log_23%2B12-log_2%5E23-5log_23-3log_23-15%3D-3 "frac{log_2192}{log_{12}2} - frac{log_224}{log_{96}2} =
log_2192log_212 - log_224log_296 =
\
=log_2(3cdot2^6)log_2(3cdot2^2) - log_2(3cdot2^3)log_2(3cdot2^5) =
\
=(log_23+log_22^6)(log_23+log_22^2) - (log_23+log_22^3)(log_23+log_22^5)
\
=(log_23+6)(log_23+2) - (log_23+3)(log_23+5) =
\
=log_2^23+2log_23+6log_23+12-log_2^23-5log_23-3log_23-15=-3")
310)
312)
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0
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