Logarithms.

Remember product rule:
`log_a X + log_a Y = log_a (X * Y)`

Subjects > Mathematics > Logarithms


Question 10:

Without using logarithms table, solve the equation:
`log (5x - 4) = log (x - 2) + 1/3 * log 27`

Solution:
Given,
`log (5x - 4) = log (x - 2) + 1/3 * log 27`
⇒ `log (5x - 4) = log (x - 2) + log 27^(1/3)`
⇒ `log (5x - 4) = log (x - 2) + log 3^(3 * 1/3)`
⇒ `log (5x - 4) = log (x -2) + log 3`
use product rule to get,
`log (5x - 4) = log 3(x - 2)`
⇒ `5x - 4 = 3(x - 2)`
⇒ `5x - 4 = 3x - 6`
⇒ `5x - 3x = -6 + 4`
⇒ `2x = -2`
⇒ `(2x)/2 = (-2)/2`
`x = -1`
∴ Value of `x` is `-1`

Sorry, it's under construction !

Sorry, it's under construction !

Skills covered in the above question

product rule of logarithms


Question 10:

Without using logarithms table, solve the equation:
`log (5x - 4) = log (x - 2) + 1/3 * log 27`

Solution:
Given,
`log (5x - 4) = log (x - 2) + 1/3 * log 27`
⇒ `log (5x - 4) = log (x - 2) + log 27^(1/3)`
⇒ `log (5x - 4) = log (x - 2) + log 3^(3 * 1/3)`
⇒ `log (5x - 4) = log (x -2) + log 3`
use product rule to get,
`log (5x - 4) = log 3(x - 2)`
⇒ `5x - 4 = 3(x - 2)`
⇒ `5x - 4 = 3x - 6`
⇒ `5x - 3x = -6 + 4`
⇒ `2x = -2`
⇒ `(2x)/2 = (-2)/2`
`x = -1`
∴ Value of `x` is `-1`

Sorry, it's under construction !

Sorry, it's under construction !

Skills covered in the above question

product rule of logarithms