What is ln((4xsqrt(1+2x))/((x-4)^3)) ?

The solution to ln((4xsqrt(1+2x))/((x-4)^3)) is 2ln(2)+ln(x)+ln(sqrt(1+2x))-3ln(x-4)

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simplify ln((4xsqrt(1+2x))/((x-4)^3))

simplify

ln (\frac{4 x 1 + 2 x}{( x - 4 ) ^{3}})

2 ln (2) + ln (x) + ln (1 + 2 x) - 3 ln (x - 4)

Solution steps

ln (\frac{4 x 1 + 2 x}{( x - 4 ) ^{3}})

Apply log rule:

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

ln (\frac{4 x 1 + 2 x}{( x - 4 ) ^{3}}) = ln (4 x 1 + 2 x) - ln ((x - 4)^{3})

= ln (4 x 2 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 (4 x 1 + 2 x) - 3 ln (x - 4)

Apply log rule:

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

ln (4 x 1 + 2 x) = ln (4) + ln (x) + ln (1 + 2 x)

= ln (4) + ln (x) + ln (2 x + 1) - 3 ln (x - 4)

ln (4) = 2 ln (2)

= 2 ln (2) + ln (x) + ln (2 x + 1) - 3 ln (x - 4)

ln (\frac{x ^{9} x ^{2} + 7}{( x + 7 ) ^{7}})

ln ∣ 436700 ∣ - ln ∣ 105400 ∣

lo g_{3} (x^{2} - 16) - 2 lo g_{3} (x + 4)

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

- lo g_{10} (8.3 \cdot 1 0^{- 5})

What is ln((4xsqrt(1+2x))/((x-4)^3)) ?
The solution to ln((4xsqrt(1+2x))/((x-4)^3)) is 2ln(2)+ln(x)+ln(sqrt(1+2x))-3ln(x-4)