### 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 !

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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

Related Lessons