Question

1. Oblicz

oraz

2. Wyznacz X

Answer 1

def log

loga b = c  ->  a^c=b

 

log₃[6*√0,75]=log₃[√36*0,75]=log₃√27=3/2

 

log₃x=log₃[8/10:16/5]

log₃x=log₃[8/10*5/16]

log₃x=log₃1/4

3^[log₃1/4]=x

x=1/4

Answer 2

1. log3 6 + log3 √(3/4) = log3 (6 * √(3/4)) = log3 (6 * √3/2) = log3 3√3 = log3 (3^1 * 3^(1/2)) = log 3^(3/2) = 3/2 * log3 3 = 3/2 * 1 = 3/2 = 1,5

 

2.

 

log3 x = log3 0,8 - log3 16/5

log3 x = log3 (0,8 : 16/5)

log3 x = log3 (8/10 * 5/16)

log3 x = log3 1/4

x = 1/4