solve logbase5(4)-logbase5(x-10)=1

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02-08-2016
Mathematics

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solve logbase5(4)-logbase5(x-10)=1

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jhonyy9 jhonyy9 · Answer 1 · 2016-08-02T02:29:26+02:00

using the property of logarithms of log(a) b - log(a) c = log(a) (b/c) you get

log5 (4) -log5 (x-10) = 1 but 1 = log5 (5) so you can rewriting your exercise

log5 (4/(x-10)) = log5 (5) what mean that these are equal than

4/(x-10) = 5 multiple the right side by (x-10) and will get

4 = 5(x-10) but first of all make the condition that x not can being equal 10 bc. than this fraction will be undefined with denominator zero

4=5(x-10) so 4 = 5x -50 add to both sides 50 and will get
4+50=5x
54=5x divide both sides by 5

x = 54/5

x = 10,8

hope helped