Преобразование логарифмических выражений
- \(\log_{\sqrt{3}}27\)
- \(\log_{2\sqrt{3}}\frac{1}{12}\)
- \(\log_9(\log_4\sqrt[3]{4})\)
- \(\log_93-3\log_{\sqrt{5}}0,2\)
- \(\log_{25}0,2+0,5\log_{\sqrt{6}}6\)
- \(\log_{\sqrt{2}}8-2\log_{1/3}9\)
- \(2\log_{\sqrt{3}}27-4\lg\sqrt{10}\)
- \(\log_33,6-\log_31,4+\log_3\frac{7}{6}\)
- \(\log_{25}64+\log_5\frac{125}{8}\)
- \(\log_3{12}-\frac{1}{\log_43}\)
- \(\log_{18}3+\frac{1}{\log_62+\log_69}\)
- \(\displaystyle\frac{\log_510+\log_210}{\log_510\cdot\log_210}\)
- \(3^{\log_94}\)
- \(49^{1-\log_72}-5^{-\log_54}\)
- \(\displaystyle\frac{\log_249}{\log_{18}7}-4\log_21,5\)
- \(\displaystyle\frac{\log_218}{\log_{36}2}-\displaystyle\frac{\log_29}{\log_{72}{2}}\)
- \(\log_311\cdot\log_{11}19\cdot\log_{19}27\)
- \(\log_23\cdot\log_34\cdot\log_45\cdot\ldots\cdot\log_{15}16\)
- Найдите \(\log_{15}49\), если \(\log_79=a\) и \(\log_745=b\)
- Найдите \(\log_{12}90\), если \(\log_{24}3=a\) и \(\log_{24}5=b\)
1) 6
2) -2
3) -1/2
4) 13/2
5) 1/2
6) 10
7) 10
8) 1
9) 3
10) 1
11) 1
12) 1
13) 2
14) 12
15) 6
16) 2
17) 3
18) 4
19) 4/(2b-a)
20) (5a+3b+1)/(a+2)