O liczbach a i b wiadomo, że [latex]9^a = 64[/latex] oraz [latex]b=log_2_7 frac{1}{8} [/latex] . Oblicz [latex]3^a^+^b[/latex].

9^a = 64 ( 3^2)^a = 64 ( 3^a)^2 = 8^2 3^a = 8 =========== b = log 27 [ 1/8] = log 27 [ (1/2)^3] = 3  log 27 ( 1/2) = 3 *(1/3) log 3(1/2) = log 3(1/2) b = log 3 [ 1/2] ================ 3^( a + b) = 3^a * 3^b = 8* 3^[ log 3 (1/2) ] = 8*(1/2) = 4 ====================================================