Question

Jika ²log 3= a dan ³log 5= b. nyatakan bentuk berikut dalam bentuk a dan b.
a. ²log 15
b. ⁴log 75
c. ²⁵log 36
d ²log 5
e ³°log 150
f ¹°°log50

thanks

Answer 1

² log 3 = a --> log 3 / log 2 =a --> log 3 = a log 2
³ log 5 =b --> log 5 / log 3= b --> log 5 = b log 3 = b ( a log 2)= ab log 2

1.) ² log 15 = ² log 3 + ² log 5 = ² log 3 + log 5/log 2 = a + ab log 2/log 2 = a +ab

2.) 4 log 75 = log 75 /log 4 = log 3 + log 25 / 2 log 2 = log 3 + 2 log 5 / 2 log 2
= a log 2+ 2 ab log 2 / 2 log 2 = log 2 (a +2ab) / 2 log 2 = a+ 2ab / 2

4.) ² log 5 = log 5 / log 2= ab log 2 / log 2 = ab