Question

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

Answer 1

 log 2 [ 3] + 3 log 16 [ 2] = log 2 [3] + log 16 [ 2^3] =

= log 2 [3] + (1/4)*log 2 [ 8 ] = log 2 [3] + log 2 [ 8^(1/4)] =

= log 2 [ 3* 8^(1/4)]

zatem

4^[ log 2 [ 3] + 3 log 16 [ 2]] =

= ( 2^2)^[ log 2 ( 3* 8^(1/4))] =

= 2 ^[ 2 *log 2 ( 3* 8^(1/4))] =

= 2^[ log 2 ( 3*8^(1/4))^2 =

= ( 3* 8^(1/4))^2 = 9 * 8^(1/2) = 9* 2 p(2) = 18 p(2)

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p(2)  - pierwiastek kwadratowy z 2