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

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

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simplify ln((5xsqrt(1+3x))/((x-4)^3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x - 4)^{3}) = 3 ln (x - 4)

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

Apply log rule:

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

ln (5 x 1 + 3 x) = ln (5) + ln (x) + ln (1 + 3 x)

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

lo g_{4} (x) + lo g_{4} (y)

14 + 7 ln (14 x - 7) - 7 ln (7 x + 1)

\frac{1}{2} lo g_{10} (b) + 9 lo g_{10} (c)

ln (\frac{2}{x})

ln (x^{6}) - ln (x)

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