Log 135 base 3/log 3 base 15 - log 5 base 3/log 3 base 405
Answers
Given:
Log 135 base 3/log 3 base 15 - log 5 base 3/log 3 base 405
To find:
Log 135 base 3/log 3 base 15 - log 5 base 3/log 3 base 405
Solution:
From given, we have,
Log 135 base 3/log 3 base 15 - log 5 base 3/log 3 base 405
Log 135 base 3/log 3 base 15 - log 5 base 3/log 3 base 405
= Log 135 base 3 × log 15 base 3 - log 5 base 3 × log 405 base 3
= Log 135 base 3 × log (5 × 3) base 3 - log 5 base 3 × log (135 × 3) base 3
= Log 135 base 3 × [log 5 base 3 + log 3 base 3] - log 5 base 3 × [log 135 base 3 + log 3 base 3]
= Log 135 base 3 × log 5 base 3 + Log 135 base 3 × log 3 base 3 - log 5 base 3 × log 135 base 3 - log 5 base 3 × log 3 base 3
= Log 135 base 3 × log 3 base 3 - log 5 base 3 × log 3 base 3
= Log 135 base 3 - log 5 base 3
= log 135/5 base 3
= log 27 base 3
= log 3³ base 3
= 3 log 3 base 3
= 3
∴ Log 135 base 3/log 3 base 15 - log 5 base 3/log 3 base 405 = 3
Answer:
Step-by-step explanation:
