Логарифмы log_6(9) + 2log_6(2) 25^(1/2+log_5(3)) 10^(2+lg5) log_3(2-x)=0 lg(x-3)=lg5+2lg3

Question

Логарифмы
log_6(9) + 2log_6(2)
25^(1/2+log_5(3))
10^(2+lg5)
log_3(2-x)=0
lg(x-3)=lg5+2lg3

Answer 1

1)
log₆9+2log₆2=log₆9+log₆2²=log₆(9*4)=log₆36=2
2)
25^(1/2+log₅3)=25^1/2*25^log₅3=5*5^log₅3²=5*3²=5*9=45
3)
10^(2+lg5)=10^2*10^lg5=100*5=500
4)
log₃(2-x)=0
log₃(2-x)=log₃1
2-x=1
x=1
5)
lg(x-3)=lg5+2lg3
lg(x-3)=lg5+lg3²
lg(x-3)=lg(5*9)
x-3=45
x=48