What is ln(e^{2x}*x*sqrt(x^4+2x^2+1)) ?

The solution to ln(e^{2x}*x*sqrt(x^4+2x^2+1)) is 2x+ln(x)+ln(sqrt(x^4+2x^2+1))

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simplify ln(e^{2x}xsqrt(x^4+2x^2+1))

simplify

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

2 x + ln (x) + ln (x^{4} + 2 x^{2} + 1)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (e^{2 x}) = 2 x ln (e)

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

2 x ln (e) = 2 x

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

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

ln (\frac{x}{x - 2})

ln (t - 1) - ln (t + 3)

6.1 + lo g_{10} (\frac{31}{0.03 \cdot 71})

\frac{9}{10} ln (30) - \frac{12}{5} ln (40)

What is ln(e^{2x}*x*sqrt(x^4+2x^2+1)) ?
The solution to ln(e^{2x}*x*sqrt(x^4+2x^2+1)) is 2x+ln(x)+ln(sqrt(x^4+2x^2+1))