CONVERT INTO SINGLE LOGARITHM EXPRESSION

Condense each expression to a single logarithm.

Problem 1 :

ln 5 + ln 7 + 2 ln 6

Solution:

= ln 5 + ln 7 + 2 ln 6

= ln 5 + ln 7 + ln 6²

= ln(5 × 7 × 6²)

= ln 1260

Problem 2 :

4 log₂ 6 + 3 log₂ 7

Solution:

= 4 log₂ 6 + 3 log₂ 7

= log₂ 6⁴ + log₂ 7³

= log₂(6⁴ × 7³)

= log₂ 444528

Problem 3 :

log₈ x + log₈ y + 6 log₈ z

Solution:

= log₈ x + log₈ y + 6 log₈ z

= log₈ x + log₈ y + log₈ z⁶

= log(xyz⁶)

Problem 4 :

18 log₉ x - 6 log₉ y

Solution:

= 18 log₉ x - 6 log₉ y

=log₉ x¹⁸ - log₉ y⁶

Problem 5 :

Solution:

Prove the following statements.

Problem 6 :

log_√b x = 2 log_b x

Solution:

log_√b x = 2 log_b x

Hence, it is proved.

Problem 7 :

Solution:

Hence, it is proved.

Problem 8 :

Solution:

Hence, it is proved.