What is expand log_{e}((xsqrt(x+1))/(2e^4)) ?

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

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expand log_{e}((xsqrt(x+1))/(2e^4))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{e} (e^{4}) = 4 lo g_{e} (e)

= lo g_{e} (x) + lo g_{e} (x + 1) - (lo g_{e} (2) + 4 lo g_{e} (e))

lo g_{e} (x) = ln (x)

lo g_{e} (x + 1) = ln (x + 1)

- (lo g_{e} (2) + 4 lo g_{e} (e)) = - (ln (2) + 4)

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

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

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

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

lo g_{10} (x) + 2 lo g_{10} (x + 1)

ln (\frac{119}{149})

ln (\frac{6}{2 \cdot π \cdot 0.2})

\frac{lo g _{10} ( a c ) + 2 lo g _{10} ( b )}{4}

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