What is ln(x)-ln(x+5)-5ln(9) ?

The solution to ln(x)-ln(x+5)-5ln(9) is ln(x/(59049(x+5)))

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simplify ln(x)-ln(x+5)-5ln(9)

simplify

ln (x) - ln (x + 5) - 5 ln (9)

ln (\frac{x}{59049 ( x + 5 )})

Solution steps

ln (x) - ln (x + 5) - 5 ln (9)

Apply log rule:

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

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

= ln (\frac{x}{x + 5}) - 5 ln (9)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 ln (9) = ln (9^{5})

= ln (\frac{x}{x + 5}) - ln (9^{5})

Apply log rule:

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

ln (\frac{x}{x + 5}) - ln (9^{5}) = ln (\frac{\frac{x}{x + 5}}{9 ^{5}})

= ln (\frac{\frac{x}{x + 5}}{9 ^{5}})

Simplify

\frac{\frac{x}{x + 5}}{9 ^{5}} : \frac{x}{59049 ( x + 5 )}

= ln (\frac{x}{59049 ( x + 5 )})

lo g_{b} (\frac{x ( x + 2 ) ^{2}}{( x - 2 ) ^{4}})

2 lo g_{3} (x) + 3 lo g_{3} (y) - 4 lo g_{3} (z)

2 ln (3) - \frac{1}{2} ln (x^{2} + 1)

lo g_{3} (9 x^{2})

\frac{1}{3} lo g_{b} (x) + 5 lo g_{b} (y) - 3 lo g_{b} (x)

What is ln(x)-ln(x+5)-5ln(9) ?
The solution to ln(x)-ln(x+5)-5ln(9) is ln(x/(59049(x+5)))