Question

Oblicz:
a) 2 log 3 + 3 log 2=
b) 3 log 4 - 4 log 2=
c) 2 log √3 + 3 log 1=
d) log log log log 10¹⁰ =
e) log₃ 6 + log₃ √0,75 =
f) log₄(3+log₃(1+log₂ 4))=
g) log₄(1+log₄(2+log₄16))=

Answer 1

a) 

2 log 3 + 3 log 2 = log 3^2 + log 2^3 = log 9 + log 8 = log (9*8 ) = log 72

b)

3 log 4 - 4 log 2 = log 4^3 - log2^4 = log 64 - log 16 = lig( 64/16) = log 4

c)

 2 log p(3) + 3 log 1 = log ( p(3))^2 + 3*0 = log 3

d)  Nie mogę odczytać wykladnika

Czy to jest 10 ?

 

e)

 log 3 ( 6) + log 3 [ p(0,75)] = log 3 ( 3*2) + log 3 [ p(3/4)] =

= log 3 (3) + log 3(2) + log 3 [ p(3)/2 ] =

= 1 + log 3(2) + log 3 [ p(3)] - log 3 (2) =

= 1 + 1/2 = 1,5

f)

log 4 [ 3 + log 3 ( 1 + log 2(4))) =

= log 4 [ 3 + log 3 ( 1 + 2)] = log 4[3 + log 3 (3)] =

= log 4 [3 + 1] = log 4 (4) = 1

 

g)  log4 [ 1 + log 4 ( 2 + log 4 (16))) =

= log 4 [ 1 + log 4 ( 2 + 2)) = log 4 [ 1 + log 4 (4)] =

= log 4 [ 1 + 1] = log 4 (2) = 1/2