1) log_(1/2)⁡16 = log16/log(1/2) = log2^4 / log2^-1 = 4 / -1 = -4
2) 5^(1+log_5⁡3 ) = 5 5^log5⁡3 = 5 3 = 15
3) log_3⁡135-log_3⁡20+2log3⁡6 = log3⁡(135 / 20) + log3⁡(6^2) = log3⁡6 + log3⁡36 = log3⁡6 + 2
4) Сравним числа:
a) log(1/2)⁡〖3/4〗 = log3/4 / log1/2 = log3 / log4 - log1 / log2 = log3 / (log2^2) - 0 = log3 / 2 = 1 / 2 log3
b) log_(1/2)⁡〖4/5〗 = log4/5 / log1/2 = log4 / log5 - log1 / log2 = log4 / log5 - 0 = log4 / log5 = log5⁡4
Так как log5⁡4 > 1/2 log3, то log(1/2)⁡〖4/5〗 > log(1/2)⁡〖3/4〗

a) log20,9 = log9 / log20 = (log3^2) / (log2 log5) = log3 / (log2 log5) = log3 / (log10) = log10^3
b) 0,1 = 1 / 10
Так как log10^3 > 1 / 10, то log20,9 > 0,1

Уравнение log_5⁡(2x-1)=2 log_2⁡(x-2)+ log_2⁡x=3 log8⁡x+log√2⁡x=14 log5(x^2-10x) = 2 + log5(2x) 7x+2 – 14 * 7x = 5
Решение уравнения требует дополнительной информации.