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brilliants [131]
2 years ago
13

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

Mathematics
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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