What is 3ln(t+5)-4ln(t)-2ln(s-1) ?

The solution to 3ln(t+5)-4ln(t)-2ln(s-1) is ln(((t+5)^3)/(t^4(s-1)^2))

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simplify 3ln(t+5)-4ln(t)-2ln(s-1)

simplify

3 ln (t + 5) - 4 ln (t) - 2 ln (s - 1)

ln (\frac{( t + 5 ) ^{3}}{t ^{4} ( s - 1 ) ^{2}})

Solution steps

3 ln (t + 5) - 4 ln (t) - 2 ln (s - 1)

Apply log rule:

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

3 ln (t + 5) = ln ((t + 5)^{3})

= ln ((t + 5)^{3}) - 4 ln (t) - 2 ln (s - 1)

Apply log rule:

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

4 ln (t) = ln (t^{4})

= ln ((t + 5)^{3}) - ln (t^{4}) - 2 ln (s - 1)

Apply log rule:

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

ln ((t + 5)^{3}) - ln (t^{4}) = ln (\frac{( t + 5 ) ^{3}}{t ^{4}})

= ln (\frac{( t + 5 ) ^{3}}{t ^{4}}) - 2 ln (s - 1)

Apply log rule:

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

2 ln (s - 1) = ln ((s - 1)^{2})

= ln (\frac{( t + 5 ) ^{3}}{t ^{4}}) - ln ((s - 1)^{2})

Apply log rule:

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

ln (\frac{( t + 5 ) ^{3}}{t ^{4}}) - ln ((s - 1)^{2}) = ln (\frac{\frac{( t + 5 ) ^{3}}{t ^{4}}}{( s - 1 ) ^{2}})

= ln (\frac{\frac{( t + 5 ) ^{3}}{t ^{4}}}{( s - 1 ) ^{2}})

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{( t + 5 ) ^{3}}{t ^{4} ( s - 1 ) ^{2}})

ln (4 x) - ln (2 x)

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ln (\frac{v}{u}) + 2 ln (d u)

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What is 3ln(t+5)-4ln(t)-2ln(s-1) ?
The solution to 3ln(t+5)-4ln(t)-2ln(s-1) is ln(((t+5)^3)/(t^4(s-1)^2))