How do you solve #\log _ { 2} x + \log _ { 4} x + \log _ { 8} x = \frac { 11} { 3}#?

1 Answer
MattyMatty
Jan 24, 2018

#x=4#

Explanation:

#log_a x = log(x)/log(a)#
#"So we have"#
#log(x)/log(2) + log(x)/log(4) + log(x)/log(8) = 11/3#
#=> log(x)/log(2) + log(x)/log(2^2) + log(x)/log(2^3) = 11/3#
#=> log(x)/log(2) + log(x)/(2 log(2)) + log(x)/(3 log(2)) = 11/3#
#=> log(x)/log(2) (1 + 1/2 + 1/3) = 11/3#
#=> log(x)/log(2) (6 + 3 + 2)/6 = 11/3#
#=> log(x)/log(2) (11/6) = 11/3#
#=> log(x) = 2 log(2)#
#=> log(x) = log(2^2)#
#=> log(x) = log(4)#
#=> x = 4#

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