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A2.
![3^{log_2frac{1}{4}+log_35}=3^{log_22^{-2}}*3^{log_35}=3^{-2}*5=frac{5}{9} 3^{log_2frac{1}{4}+log_35}=3^{log_22^{-2}}*3^{log_35}=3^{-2}*5=frac{5}{9}](https://tex.z-dn.net/?f=3%5E%7Blog_2frac%7B1%7D%7B4%7D%2Blog_35%7D%3D3%5E%7Blog_22%5E%7B-2%7D%7D%2A3%5E%7Blog_35%7D%3D3%5E%7B-2%7D%2A5%3Dfrac%7B5%7D%7B9%7D)
A3.
![log_6sqrt{a}=4\log_6a^frac{1}{2}=4\frac{1}{2}log_6a=4\log_6a=8\frac{1}{log_a6}=8\log_a6=frac{1}{8}=0.125 log_6sqrt{a}=4\log_6a^frac{1}{2}=4\frac{1}{2}log_6a=4\log_6a=8\frac{1}{log_a6}=8\log_a6=frac{1}{8}=0.125](https://tex.z-dn.net/?f=log_6sqrt%7Ba%7D%3D4%5Clog_6a%5Efrac%7B1%7D%7B2%7D%3D4%5Cfrac%7B1%7D%7B2%7Dlog_6a%3D4%5Clog_6a%3D8%5Cfrac%7B1%7D%7Blog_a6%7D%3D8%5Clog_a6%3Dfrac%7B1%7D%7B8%7D%3D0.125)
A4.
![(12^{1-2log_{12}6}+7^{-2log_{49}6})^{-1}=(12*(12^{log_{12}6})^{-2}+(49^{log_{49}6})^{-1})^{-1}=\=(12*frac{1}{36}+frac{1}{6})^{-1}=(frac{2}{6}+frac{1}{6})^{-1}=2 (12^{1-2log_{12}6}+7^{-2log_{49}6})^{-1}=(12*(12^{log_{12}6})^{-2}+(49^{log_{49}6})^{-1})^{-1}=\=(12*frac{1}{36}+frac{1}{6})^{-1}=(frac{2}{6}+frac{1}{6})^{-1}=2](https://tex.z-dn.net/?f=%2812%5E%7B1-2log_%7B12%7D6%7D%2B7%5E%7B-2log_%7B49%7D6%7D%29%5E%7B-1%7D%3D%2812%2A%2812%5E%7Blog_%7B12%7D6%7D%29%5E%7B-2%7D%2B%2849%5E%7Blog_%7B49%7D6%7D%29%5E%7B-1%7D%29%5E%7B-1%7D%3D%5C%3D%2812%2Afrac%7B1%7D%7B36%7D%2Bfrac%7B1%7D%7B6%7D%29%5E%7B-1%7D%3D%28frac%7B2%7D%7B6%7D%2Bfrac%7B1%7D%7B6%7D%29%5E%7B-1%7D%3D2)
A3.
A4.
Ответ дал:
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2)![3^{-2log(2)2} * 3^{log(3)5} = 3^{-2} *5=1/9*5=5/9 3^{-2log(2)2} * 3^{log(3)5} = 3^{-2} *5=1/9*5=5/9](https://tex.z-dn.net/?f=+3%5E%7B-2log%282%292%7D+%2A+3%5E%7Blog%283%295%7D+%3D+3%5E%7B-2%7D+%2A5%3D1%2F9%2A5%3D5%2F9)
3)log(6)√2=4⇒1/2log(6)a=4⇒log(6)a=8
log(a)6=1/log(6)a=1/8=0,125
4)![(12:12 ^{log(12)36} +49 ^{log(49)1/6} ) ^{-1} =(12:36+1/6) ^{-1} =(1/3+1/6) ^{-1} = (12:12 ^{log(12)36} +49 ^{log(49)1/6} ) ^{-1} =(12:36+1/6) ^{-1} =(1/3+1/6) ^{-1} =](https://tex.z-dn.net/?f=%2812%3A12+%5E%7Blog%2812%2936%7D+%2B49+%5E%7Blog%2849%291%2F6%7D+%29+%5E%7B-1%7D+%3D%2812%3A36%2B1%2F6%29+%5E%7B-1%7D+%3D%281%2F3%2B1%2F6%29+%5E%7B-1%7D+%3D)
3)log(6)√2=4⇒1/2log(6)a=4⇒log(6)a=8
log(a)6=1/log(6)a=1/8=0,125
4)
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