How do you solve #2log_2 (x )+ log_2 (1)= log_2 (4)#?

1 Answer
Karthik G
Dec 24, 2015

Step by step explanation is given below.

Explanation:

#2log_2(x)+log_2(1) = log_2(4)#

Let us use rules of logarithms

#1. log_b (1) = 0# #log(1)# to any base is zero
#2. log_b (a^n) = n log_b(a) #
#3. log_b (A) = log_b (C) => A= C#

#2log_2(x)+0 = log_2(2^2)# by rule 1 and rewriting 4 as 2^2

#2log_2(x) = 2log_2(2)# by rule 2
#log_2(x) = log_2(2) # After dividing by 2 on both sides.
#x = 2# by rule 3.

The solution is #x=2#

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