What is 9ln(t)+ln(y)-ln(y+1) ?

The solution to 9ln(t)+ln(y)-ln(y+1) is ln((t^9y)/(y+1))

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simplify 9ln(t)+ln(y)-ln(y+1)

simplify

9 ln (t) + ln (y) - ln (y + 1)

ln (\frac{t ^{9} y}{y + 1})

Solution steps

9 ln (t) + ln (y) - ln (y + 1)

Apply log rule:

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

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

= ln (t^{9}) + ln (y) - ln (y + 1)

Apply log rule:

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

ln (t^{9}) + ln (y) = ln (t^{9} y)

= ln (t^{9} y) - ln (y + 1)

Apply log rule:

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

ln (t^{9} y) - ln (y + 1) = ln (\frac{t ^{9} y}{y + 1})

= ln (\frac{t ^{9} y}{y + 1})

lo g_{3} (\frac{c}{9})

lo g_{2} (\frac{1}{3}) + lo g_{4} (9)

lo g_{10} (\frac{2 x}{1 + x ^{2}})

lo g_{b} (\frac{a}{h})

lo g_{w} (\frac{7 x}{4})

What is 9ln(t)+ln(y)-ln(y+1) ?
The solution to 9ln(t)+ln(y)-ln(y+1) is ln((t^9y)/(y+1))