Question

1. Jeśli log8k =5/3 to ...

poprawna odpowiedż to k = 32

2. Syma log5 125 + log4 16 do potegi 2 jest równa ...

poprawna odpowiedż to 7

3.Oblicz

A: log49 7 , log17 1 , log 100 000

B: log0,2 625 , log pierwiastek z 3 27 , log16 2

Proszę o szybką pomoc ;/

Answer 1

z.1

 

log 8 [ k] = 5/3

k = 8^(5/3) = [ 8 ^(1/3)]^5 = 2^5 = 32

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z.2

log 5 [ 125 ] + log 4 [16^2] = 3 + 2* log 4 [16] = 3 + 2*2 = 3 + 4 = 7

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z.3

a)

log 49 [ 7 ] = 1/2 , bo  49^(1/2) = 7

log 17 [ 1] = 0,  bo 17^0 = 1

log 100 000 = 5,  bo  10^5 = 100 000

b)

log 0,2 [ 625] = log 1/5 [ 5^4] = 4* log 1/5 [ 5] = 4*(-1) = - 4

bo  ( 1/5)^(-1) = 5

log p(3) [ 27 ] = log p(3) [ 3^3] = 3* log p(3)[ 3] = 3*2 = 6

bo  p(3)^2 = 3

log 16 [ 2 ] = (1/4) log 2 [2] = (1/4)*1 = 1/4

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Answer 2