What is expand ln((xsqrt(x+1))/(2e^4)) ?

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

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expand ln((xsqrt(x+1))/(2e^4))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x x + 1) = ln (x) + ln (x + 1), ln (2 e^{4}) = ln (2) + ln (e^{4})

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

Apply log rule:

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

ln (e^{4}) = 4 ln (e)

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

4 ln (e) = 4

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

- (ln (2) + 4) : - ln (2) - 4

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

lo g_{2} (x + 2) - lo g_{2} (x - 2)

lo g_{2} (\frac{x ^{3}}{x + 5})

- \frac{18 ln ( 2 )}{ln ( \frac{8}{5} )}

ln (5) + 3 ln (x) + 5 ln (x^{2} + 6)

lo g_{5} (\frac{x y}{z t})

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