How do you solve this logarithmic equation? $3log_(5)x-log_(5)(5x)=3-log_(5)25$

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Answer 1 · 2017-01-08T00:20:34

${5}$

Put all logarithms to one side:

$3log_5 x - log_5 (5x) + log_5 25 = 3$

$log_5 25$ can be rewritten as $(log25)/(log5) = (2log5)/(log5) = 2$

$log_5 x^3 - log_5 (5x) + 2 = 3$

$log_5 x^3 - log_5 5x = 1$

$log_5((x^3)/(5x)) = 1$

$x^2/5 = 5^1$

$x^2 = 25$

$x = +- 5$

The $-5$ solution is extraneous, since $log_5(ax)$ , where $a$ is a positive constant is only defined in the positive-x-values.

Hopefully this helps!

How do you solve this logarithmic equation? 3log_(5)x-log_(5)(5x)=3-log_(5)253log_(5)x-log_(5)(5x)=3-log_(5)25