Question

Logarytmy! Prosze o pomoc w rozwiazaniu tych zadan. ODpowiedzi koniecznie z rozwiazaniami! Plisss PILNE!!!!

Answer 1

9.

 

3^x = 12

3^x = 3 * 4    /:3

3^x / 3 = 4

3^(x - 1) = 4

odp. A

3^(x - 1) = 2^2

log 3^(x  -1) = log 2^2

(x - 1)log 3 = 2log 2

xlog 3 - log 3 = 2log 2

xlog 3 = log 2^2 + log 3

xlog 3 = log (4 * 3)

x log 3 = log 12

x = log 12 / log 3

x = log3 12

odp. C

 

x = log3 12

x = log3 (3 * 4)

x = log3 3 + log3 4

x = 1 + log3 2^2

x - 1 = 2log3 2

(x - 1) / 2 = log3 2

odp. B

 

10.

y = loga x

Mamy tam punkt (4, 1)

                                 x  y

loga 4 = 1

a^1 = 4

a^1 = 4^1

a = 4

 

y = log4 x   ----- taki mamy wykres

x = 16 to  y = log4 16 = log4 4^2 = 2 log4 4 = 2 * 1 = 2

odp. A

 

f(3x) = log4 (3x) = log4 (3 * 1) = log4 3

f(4 - x) = log4 (4 - x) = log4 (4 - 1) = log4 3

odp. C