Question

Zadania w załączniku. Proszę o pomoc. :c

Answer 1

4.

a)

(1/5)^x = 125^(-2)

(1/5)^x = (1/125)^2

(1/5)^x = [ (1/5)^3 ]^2

(1/5)^x = (1/5)^6

x = 6

 

b)

log1/2 x + log1/2 3 = log1/2 5

log1/2 (x * 3) = log1/2 5

3x = 5

x = 5/3

x = 1 i 2/3

 

c)

log(1-x) 8 = 3          x≠ 1

(1 - x)^3 = 8

(1 - x)^3 = 2^3

1 - x = 2

-x = 2 - 1

-x = 1

x = -1

 

3.

a)

.... = log1/3 3^3 * 3^(1/2) = log1/3 3^(3 i 1/2) = log1/3 (1/3)^(-3 ,5) = -3,5

b)

.... = log2 (4 * 7 : 14) = log2 (28 : 14) = log2  2 = 1

c)

.... = (3^4)^log3 √2 = 3^log3 (√2)^4 = 3^log3 4 = 4

d)

..... =[ 5^(1/2) * (√5³)³] : 5  = [ 5^(1/2) * (5^(1/3))^3 ] : 5 = [ 5^(1/2) * 5 ] : 5 = √5

 

2.

y = a^x                A = (-4, 16)

                                    x      y

16 = a^(-4)

2^4 = (1/a)4

2 = 1/a

2a = 1

a = 1/2

 

y = (1/2)^x    ----  wzór funkcji

 

1.

(1/3)^π = 3^(-π)

27^(-2/3√3) = 3^(3 * (-2/3√3)) = 3^(-2√3)

(1/9)^(-3/8) = 9^(3/8) = 3^(2 * 3/8) = 3^(3/4)

9^(π/6) = 3^(2 * π/6) = 3^(π/3)

(1/3)^(-2√3) = 3^(2√3)