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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Subjects > Mathematics > Logarithms


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 !

Skills covered in the above question

Product rule of logarithms Power rule of logarithms


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 !

Skills covered in the above question

Product rule of logarithms

Power rule of logarithms