Exercise 3.5
Q.1: Use logarithm properties to simplify the expression
i) 𝐥𝐨𝐠 𝟕 √𝟕
ii) 𝐥𝐨𝐠 𝟖
𝟏
𝟐
iii) 𝐥𝐨𝐠 𝟏𝟎 √𝟏𝟎𝟎𝟎
𝐥𝐨𝐠 𝟗 𝟐𝟕
iv) 𝐥𝐨𝐠 𝟗 𝟑 +
𝟏
v) 𝐥𝐨𝐠 (𝟎.𝟎𝟎𝟑𝟓)−𝟒
vi) 𝐥𝐨𝐠 𝟒𝟓
Q.2: Express each of the following as a single logarithm.
i)
𝟑 𝐥𝐨𝐠 𝟐 − 𝟒 𝐥𝐨𝐠 𝟑
ii) 𝟐 𝐥𝐨𝐠 𝟑 + 𝟒 𝐥𝐨𝐠 𝟐 − 𝟑
iii)
𝐥𝐨𝐠 𝟓 − 𝟏
𝟏
iv) 𝐥𝐨𝐠 𝒙 − 𝟐 𝐥𝐨𝐠 𝟑𝒚 + 𝟑 𝐥𝐨𝐠 𝒛
𝟐
Q3: Find the value of ′𝑎′ from the following equations.
i)
𝐥𝐨𝐠 𝟐 𝟔 + 𝐥𝐨𝐠 𝟐 𝟕 = 𝐥𝐨𝐠 𝟐 𝒂
ii)
𝐥𝐨𝐠 √𝟑 𝒂 = 𝐥𝐨𝐠 √𝟑 𝟓 + 𝐥𝐨𝐠 √𝟑 𝟖 − 𝐥𝐨𝐠 √𝟑 𝟐
iii)
𝐥𝐨𝐠 𝟕 𝒓
𝐥𝐨𝐠 𝟕 𝒕
= 𝐥𝐨𝐠 𝒂 𝒓
iv)
𝐥𝐨𝐠 𝟔 𝟐𝟓 − 𝐥𝐨𝐠 𝟔 𝟓 = 𝐥𝐨𝐠 𝟔 𝒂
Q,4: Find
𝐥𝐨𝐠 𝟐 𝟑 . 𝐥𝐨𝐠 𝟑 𝟒 . 𝐥𝐨𝐠 𝟒 𝟓 . 𝐥𝐨𝐠 𝟓 𝟔 . 𝐥𝐨𝐠 𝟔 𝟕 . 𝐥𝐨𝐠 𝟕 𝟖