How do you combine #2\log _ { 4} ( x ) + 3\log _ { 4} ( 3) - \log _ { 4} ( 7)#?

1 Answer
sankarankalyanam
Jan 26, 2018

#color(green)(= log_4 ((27x^2)/7))#

Explanation:

Basic rules of logarithms when bases are the same.

  1. #log A + log B = log AB#

  2. #log A − log B = log (A/B)#

  3. #log A^n = n log A#

  4. #log 1 = 0,#

  5. #log_m m = 1#

Given : #2 log_4 x + 3 log_4 3 - log_4 7#

= #log _4 x^2 + log_4 3^2 - log_4 7# using Rue 3.

#= log_4 (x^2 * 3^3) - log_4 7# using Rule 1

#= log_4 ((x^2 * 3^3)/7)# using Rule 2

#= log_4 ((27x^2) / 7)#

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