What is ln((sqrt(x+13))/((x-4)^3sqrt(2x+1))) ?

The solution to ln((sqrt(x+13))/((x-4)^3sqrt(2x+1))) is ln(sqrt(x+13))-3ln(x-4)-ln(sqrt(2x+1))

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simplify ln((sqrt(x+13))/((x-4)^3sqrt(2x+1)))

simplify

ln (\frac{x + 13}{( x - 4 ) ^{3} 2 x + 1})

ln (x + 13) - 3 ln (x - 4) - ln (2 x + 1)

Solution steps

ln (\frac{x + 13}{( x - 4 ) ^{3} 2 x + 1})

Apply log rule:

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

ln (\frac{x + 13}{( x - 4 ) ^{3} 2 x + 1}) = ln (x + 13) - ln ((x - 4)^{3} 2 x + 1)

= ln (x + 13) - ln ((x - 4)^{3} 2 x + 1)

Apply log rule:

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

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

= ln (x + 13) - (ln ((x - 4)^{3}) + ln (2 x + 1))

Apply log rule:

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

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

= ln (x + 13) - (3 ln (x - 4) + ln (2 x + 1))

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

= ln (x + 13) - 3 ln (x - 4) - ln (2 x + 1)

ln (\frac{1.2}{1.5})

- ln (60 - X) + ln (150 - X)

10 \cdot lo g_{e} (\frac{e - 1}{e})

20 lo g_{10} (0.1) + 20 lo g_{10} (2.4) + 92.45

What is ln((sqrt(x+13))/((x-4)^3sqrt(2x+1))) ?
The solution to ln((sqrt(x+13))/((x-4)^3sqrt(2x+1))) is ln(sqrt(x+13))-3ln(x-4)-ln(sqrt(2x+1))