What is ln((sqrt(x))/x)+ln(\sqrt[4]{ex^2}) ?

The solution to ln((sqrt(x))/x)+ln(\sqrt[4]{ex^2}) is 1/4

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simplify ln((sqrt(x))/x)+ln(\sqrt[4]{ex^2})

simplify

\frac{1}{4}

Decimal Notation

0.25

Solution steps

Apply log rule:

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

Rewrite as

= ln (e^{\frac{1}{4}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{4} ln (e)

Apply log rule:

lo g_{a} (a) = 1

= \frac{1}{4}

lo g_{111} (\frac{20000}{111}) + 1

ln (\frac{27027}{625})

\frac{1}{5} ln (y) + ln (z)

2 (ln (x) + ln (3)) - 3 ln (y)

lo g_{3} (x) + lo g_{3} (5 y)

What is ln((sqrt(x))/x)+ln(\sqrt[4]{ex^2}) ?
The solution to ln((sqrt(x))/x)+ln(\sqrt[4]{ex^2}) is 1/4