What is ln(3x+5)-4ln(x)-ln(x-1) ?

The solution to ln(3x+5)-4ln(x)-ln(x-1) is ln((3x+5)/(x^4(x-1)))

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simplify ln(3x+5)-4ln(x)-ln(x-1)

simplify

ln (3 x + 5) - 4 ln (x) - ln (x - 1)

ln (\frac{3 x + 5}{x ^{4} ( x - 1 )})

Solution steps

ln (3 x + 5) - 4 ln (x) - ln (x - 1)

Apply log rule:

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

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

= ln (3 x + 5) - ln (x^{4}) - ln (x - 1)

Apply log rule:

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

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

= ln (\frac{3 x + 5}{x ^{4}}) - ln (x - 1)

Apply log rule:

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

ln (\frac{3 x + 5}{x ^{4}}) - ln (x - 1) = ln (\frac{\frac{3 x + 5}{x ^{4}}}{x - 1})

= ln (\frac{\frac{3 x + 5}{x ^{4}}}{x - 1})

Apply the fraction rule:

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

= ln (\frac{3 x + 5}{x ^{4} ( x - 1 )})

lo g_{3} (8 x)

ln (4 e^{3})

ln ((1 - 3 i)^{3})

lo g_{10} (5 x + 9) - lo g_{10} (x)

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

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