# CONVERT INTO SINGLE LOGARITHM EXPRESSION

## Properties of logarithms :

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 logb x

Solution:

log√b x = 2 logb x

Hence, it is proved.

Problem 7 :

Solution:

Hence, it is proved.

Problem 8 :

Solution:

Hence, it is proved.

## Recent Articles

1. ### Finding Range of Values Inequality Problems

May 21, 24 08:51 PM

Finding Range of Values Inequality Problems

2. ### Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Solving Two Step Inequality Word Problems