Question

Oblicz: A) log2 1/32 B) log0,5 64 C) log4 400 - 2log4 5

Answer 1

a)

log 2 ( 1/32) = - 5, bo  2 ^(-5) = 1/( 2^5) = 1/32

b)

log 0,5 ( 64) = log 1/2 ( 64) = - 6, bo (1/2)^( -6) = 2^6 = 64

c)

log 4 ( 400 ) - 2 log 4 ( 5) = log 4 ( 400) - log 4 ( 5^2) = log 4 ( 400) - log 4( 25) =

= log 4 ( 400/25) = log 4 ( 16) = 2  , bo  4^2 = 16

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Answer 2

a) log2 (1/32) = log2 (1/2)^5 = log2 2^(-5) = -5 * log2 2 = -5 * 1 = -5

b) log0,5 (64) = log1/2 2^6 = log1/2 (1/2)^(-6) = -6 * log1/2 1/2 = -6

c) log4 (400) - 2 log4 5 = log4 400 - log4 5^2 =log4 400 - log4 25 =

log4 (400/25) = log4 16  = log4 4^2 = 2 * log4 4 = 2 * 1 = 2 

 

wzory:

loga b^n = n * loga b

loga b - loga c = loga (b / c)