What is ln(x)+ln(x+3)-ln(20-5x) ?

The solution to ln(x)+ln(x+3)-ln(20-5x) is ln((x(x+3))/(20-5x))

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simplify ln(x)+ln(x+3)-ln(20-5x)

simplify

ln (x) + ln (x + 3) - ln (20 - 5 x)

ln (\frac{x ( x + 3 )}{20 - 5 x})

Solution steps

ln (x) + ln (x + 3) - ln (20 - 5 x)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x) + ln (x + 3) = ln (x (x + 3))

= ln (x (x + 3)) - ln (20 - 5 x)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x (x + 3)) - ln (20 - 5 x) = ln (\frac{x ( x + 3 )}{- 5 x + 20})

= ln (\frac{x ( x + 3 )}{20 - 5 x})

ln (\frac{5 + e ^{x}}{5 - e ^{x}})

\frac{1}{2} lo g_{6} (3)

ln (sec (x)) + ln (x)

lo g_{10} (2 x - 3) - lo g_{10} (e)

lo g_{3} (x - 3) + lo g_{3} (x - 2)

What is ln(x)+ln(x+3)-ln(20-5x) ?
The solution to ln(x)+ln(x+3)-ln(20-5x) is ln((x(x+3))/(20-5x))