What is ln(sqrt(x)e^x)+ln((sqrt(x))/(e^x)) ?

The solution to ln(sqrt(x)e^x)+ln((sqrt(x))/(e^x)) is ln(x)

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simplify ln(sqrt(x)e^x)+ln((sqrt(x))/(e^x))

simplify

ln (x e^{x}) + ln (\frac{x}{e ^{x}})

ln (x)

Solution steps

ln (x e^{x}) + ln (\frac{x}{e ^{x}})

Apply log rule:

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

ln (e^{x} x) + ln (\frac{x}{e ^{x}}) = ln (e^{x} x \frac{x}{e ^{x}})

= ln (e^{x} x \frac{x}{e ^{x}})

Simplify

x e^{x} \frac{x}{e ^{x}} : x

= ln (x)

lo g_{10} (\frac{x 3 z ^{2}}{y ^{5}})

lo g_{10} (x) - (lo g_{10} (y) - 5 lo g_{10} (x^{2}))

lo g_{6} (A B^{6})

lo g_{5} (8 yz)

ln (2 x) + ln (1)

What is ln(sqrt(x)e^x)+ln((sqrt(x))/(e^x)) ?
The solution to ln(sqrt(x)e^x)+ln((sqrt(x))/(e^x)) is ln(x)