What is ln((x^8sqrt(x-6))/(4x+5)) ?

The solution to ln((x^8sqrt(x-6))/(4x+5)) is 8ln(x)+ln(sqrt(x-6))-ln(4x+5)

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simplify ln((x^8sqrt(x-6))/(4x+5))

simplify

ln (\frac{x ^{8} x - 6}{4 x + 5})

8 ln (x) + ln (x - 6) - ln (4 x + 5)

Solution steps

ln (\frac{x ^{8} x - 6}{4 x + 5})

Apply log rule:

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

ln (\frac{x ^{8} x - 6}{4 x + 5}) = ln (x^{8} x - 6) - ln (4 x + 5)

= ln (x^{8} x - 6) - ln (4 x + 5)

Apply log rule:

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

ln (x^{8} x - 6) = ln (x^{8}) + ln (x - 6)

= ln (x^{8}) + ln (x - 6) - ln (4 x + 5)

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= 8 ln (x) + ln (x - 6) - ln (4 x + 5)

\frac{1}{2} lo g_{7} (4 m^{2})

lo g_{10} (\frac{7 x + 3}{x ^{4} ( x - 5 ) ^{2}})

lo g_{6} (x + 3) + lo g_{6} (x^{2} - 4) - lo g_{6} (x + 2)

lo g_{2} (4) + lo g_{2} (6) + lo g_{2} (3)

lo g_{3} (3 x)

What is ln((x^8sqrt(x-6))/(4x+5)) ?
The solution to ln((x^8sqrt(x-6))/(4x+5)) is 8ln(x)+ln(sqrt(x-6))-ln(4x+5)