Question

Oblicz: 4 i reszta w potedze: log2 3+log16 2

Answer 1

log  2[ 3] + log 16 [ 2 ] = log 2 [3] + (1/4) log 2 [ 2] = log2 [3] + log2 [ 2^(1/4)] =

= log2 [ 3*2^(1/4)]

zatem

4^[ log 2 ( 3* 2^(1/4))] = (2^2)^[ log 2 ( 3*2^(1/4))] =

= 2^[ 2* log 2 ( 3*2^(1/4))] = 2^log 2 [ ( 3* 2^(1/4))^2] =

= [ 3*2^(1/4)]^2 = 3^2 * [ 2^(1/4)]^2 = 9* 2^(1/2) = 9 p(2)

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p(2)  - pierwiastek kwadratowy z 2