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brilliants [131]

2 years ago

13

Log base 5 (3) - log base 5 (5x) = 2

1 answer:

Sladkaya [172]2 years ago

5 0

The answer is 3/125

$log_a(x) - log_a(y)=log_a( \frac{x}{y} ) \\ 
log_5(3) - log_5(5x) = log_5( \frac{3}{5x})$

$log_5( \frac{3}{5x})=2$

Since $log_b(x)=y$ is $b^{y} =x$ , then:
$log_5( \frac{3}{5x})=2$ is
$5^{2} = \frac{3}{5x} \\ 25 = \frac{3}{5x} \\ 5x*25=3 \\ 125x=3 \\ x=3/125$

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