How do you solve #2\log _ { 5} ( x ) - \log _ { 5} ( 5) = \log _ { 5} ( 125)#?

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Answer 1 · 2018-01-26T08:18:27

#color(green)(x = 5)#

Laws of Logarithms

Given : #2 log_5 x - log_5 5 = log_5 125#

#log_5 x^2 = log_5 5 + log_5 125# using Law 3.

#log_x^2 = log_5 5 + log _5 5^3# using Law 3

#log_5 x^2 = log_5 (5*125) = log_5 625# using Law 1

#log_5x^2 = log_5 (25)^2#

Removing log on both sides,

#x^2 = 25^2#, Taking square root on both sides,

#color(green)(x = 5)#

Answer 2 · 2018-01-26T13:52:41

#x=25#

#2log_5x-log_5(5)=log_5(125)#

#2log_5x-1=3#

#2log_5x=4#

#log_5x=2#

#x=5^2=25#