What is ln((7xsqrt(1+6x))/((x-4)^4)) ?

The solution to ln((7xsqrt(1+6x))/((x-4)^4)) is ln(7)+ln(x)+ln(sqrt(1+6x))-4ln(x-4)

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simplify ln((7xsqrt(1+6x))/((x-4)^4))

simplify

ln (\frac{7 x 1 + 6 x}{( x - 4 ) ^{4}})

ln (7) + ln (x) + ln (1 + 6 x) - 4 ln (x - 4)

Solution steps

ln (\frac{7 x 1 + 6 x}{( x - 4 ) ^{4}})

Apply log rule:

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

ln (\frac{7 x 1 + 6 x}{( x - 4 ) ^{4}}) = ln (7 x 1 + 6 x) - ln ((x - 4)^{4})

= ln (7 x 6 x + 1) - ln ((x - 4)^{4})

Apply log rule:

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

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

= ln (7 x 1 + 6 x) - 4 ln (x - 4)

Apply log rule:

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

ln (7 x 1 + 6 x) = ln (7) + ln (x) + ln (1 + 6 x)

= ln (7) + ln (x) + ln (6 x + 1) - 4 ln (x - 4)

lo g_{3} ((u^{4} v)^{6})

ln (\frac{1}{2 ^{n}})

2 lo g_{5} (3) - \frac{1}{2} lo g_{5} (4) + lo g_{5} (8)

lo g_{4} (\frac{7}{x ^{3}})

lo g_{e} (\frac{- 0.15}{0.0075500000000 \dots})

What is ln((7xsqrt(1+6x))/((x-4)^4)) ?
The solution to ln((7xsqrt(1+6x))/((x-4)^4)) is ln(7)+ln(x)+ln(sqrt(1+6x))-4ln(x-4)