What is x if #log(x+10) -log (3x-8)= 2#?

1 Answer
Mar 11, 2018

Answer:

see a solution step below..

Explanation:

#log(x + 10) - log(3x - 8) = 2#

Recall the law of logarithm..

#loga - logb = loga/logb#

Hence;

#log(x + 10)/log(3x - 8) = 2 -> "applying law of logarithm"#

#log[(x + 10)/(3x - 8)] = 2#

For every log, there is a base, and it's default base is #10#, since there was no actual base specified in the given question..

Therefore;

#log_10 [(x + 10)/(3x - 8)] = 2#

Recall again the law of logarithm..

#log_a x = y rArr x = a^y#

Hence;

#(x + 10)/(3x - 8) = 10^2 -> "applying law of logarithm"#

#(x + 10)/(3x - 8) = 100#

#(x + 10)/(3x - 8) = 100/1#

#1(x + 10) = 100(3x - 8) -> "cross multiplying"#

#x + 10 = 300x - 800#

#300x - 800 = x + 10 -> "rearranging the equation"#

#300x - x = 10 + 800 ->"collecting like terms"#

#299x = 810#

#x = 810/299 -> "diving both sides by the coefficient of x"#

#x = 2.70#