### Logarithms.

is the inverse function to exponentation, as it answers the question, how many of one number do we multiply to get another number.
loga x = log of x to base a.
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Question 01:

Evaluate: log_5 2 + log_5 50 - log_5 4

###### Solution:
Given:
log_5 2 + log_5 50 - log_5 4
since both terms have common base 5, then
⇒ (log_5 2 + log_5 50) - log_5 4
use product rule to get,
log_5 (2 x 50) - log_5 4
⇒ log_5 100 - log_5 4
now, use quotient rule to get,
log_5 (100/4)
⇒ log_5 25
⇒ log_5 5^2 = 2log_5 5
but log_5 5 = 1
Hence,
⇒ 2log_5 5 = 2 x 1 = 2

∴ log_5 2 + log_5 50 - log_5 4 = 2

Sorry, it's under construction !

Sorry, it's under construction !

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Question 01:

Evaluate: log_5 2 + log_5 50 - log_5 4

###### Solution:
Given:
log_5 2 + log_5 50 - log_5 4
since both terms have common base 5, then
⇒ (log_5 2 + log_5 50) - log_5 4
use product rule to get,
log_5 (2 x 50) - log_5 4
⇒ log_5 100 - log_5 4
now, use quotient rule to get,
log_5 (100/4)
⇒ log_5 25
⇒ log_5 5^2 = 2log_5 5
but log_5 5 = 1
Hence,
⇒ 2log_5 5 = 2 x 1 = 2

∴ log_5 2 + log_5 50 - log_5 4 = 2

Sorry, it's under construction !

Sorry, it's under construction !

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