EXPANDING LOGARITHMIC EXPRESSIONS

Write the following expressions in terms of logs of x, y and z.

Problem 1 :

log x²y

Solution:

= log₁₀ (x²y)

= log₁₀ x² + log₁₀ y

= 2 log₁₀ x + log₁₀ y

Problem 2 :

Solution:

Problem 3 :

log xyz

Solution:

= log₁₀ xyz

= log₁₀ x + log₁₀ y + log₁₀ z

Problem 4 :

Solution:

Problem 5 :

Solution:

Expand each logarithm.

Problem 6 :

Solution:

Problem 7 :

log₆(u⁴v⁴)

Solution:

= log₆(u⁴v⁴)

= log₆ u⁴ + log₆ v⁴

= 4 log₆ u + 4 log₆ v

Problem 8 :

Solution:

Problem 9 :

log₄(u⁶v⁵)

Solution:

= log₄(u⁶v⁵)

= log₄ u⁶ + log₄ v⁵

= 6 log₄ u + 5 log₄ v

Problem 10 :

Solution: