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

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