If log5 x - log5(x - 2) = 3, then the value of x, to the nearest hundredth, is?

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Answer 1 · 2017-01-13T00:21:37

$x ~= 2.02$ (Assuming $log5$ represents $log_5$ )

Assuming $log5$ represents $log_5$ (log to the base 5), we have:

$log_5x-log_5(x-2)=3$

$log_5(x/(x-2)) =3$

$x/(x-2) = 5^3 = 125$

$x=125(x-2)$

$124x = 250$

$x=250/124 ~= 2.02$ (To the nearest hundredth as requested)

However, to perform a check you should use 8 decimal places:
$x~= 2.01612903$