Ответ:
Объяснение:
![\displaystyle\\\log_{51}x=log_{51}lg1000+log_{51}17=log_{51}lg10^3+log_{51}17=\\ \\=log_{51}3+log_{51}17=log_{51}(3*17)=log_{51}51\\ \\ x=51\\ \\](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5C%5Clog_%7B51%7Dx%3Dlog_%7B51%7Dlg1000%2Blog_%7B51%7D17%3Dlog_%7B51%7Dlg10%5E3%2Blog_%7B51%7D17%3D%5C%5C%20%5C%5C%3Dlog_%7B51%7D3%2Blog_%7B51%7D17%3Dlog_%7B51%7D%283%2A17%29%3Dlog_%7B51%7D51%5C%5C%20%5C%5C%20x%3D51%5C%5C%20%5C%5C)
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![\displaystyle\\log_ca+log_cb=log_c(a*b)\\ \\ log_aa^n=n\\ \\](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5Clog_ca%2Blog_cb%3Dlog_c%28a%2Ab%29%5C%5C%20%5C%5C%20log_aa%5En%3Dn%5C%5C%20%5C%5C)
Отрицательная степень означает деление.
1) (1/2)^(5x-9) = 1*2⁹ / 2^(5x)
1*2⁹ / 2^(5x) = 1/2⁶
Отсюда получаем 2^(5x) = 2^(9+6)
2^(5x) = 2¹⁵
5x = 15 x = 3
2) (1/2)^(6-2x) = 2²
1*2^(2x) / 2⁶ = 2²
2^(2x) = 2⁶ * 2²
2^(2x) = 2⁸
2x = 8 x = 4
3) (1/7)^(5x-3) = 1/7²
7³ / 7^(5x) = 1 / 7²
7^(5x) = 7⁵
5x = 5 x = 1
4) (1/3)^(8-3x) = 3⁴
3^(3x) = 3¹²
3x = 12 x = 4
4x-(7x-2)=17
4x-7x+2=17
-3x=15
X=-5