What is ln((7^{3/4})/7) ?

The solution to ln((7^{3/4})/7) is -1/4 ln(7)

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simplify ln((7^{3/4})/7)

simplify

ln (\frac{7 ^{\frac{3}{4}}}{7})

- \frac{1}{4} ln (7)

Decimal Notation

- 0.48647 \dots

Solution steps

ln (\frac{7 ^{\frac{3}{4}}}{7})

Apply log rule:

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

ln (\frac{7 ^{\frac{3}{4}}}{7}) = ln (7^{\frac{3}{4}}) - ln (7)

= ln (7^{\frac{3}{4}}) - ln (7)

Apply log rule:

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

ln (7^{\frac{3}{4}}) = \frac{3}{4} ln (7)

= \frac{3}{4} ln (7) - ln (7)

Factor out common term

ln (7)

= ln (7) (\frac{3}{4} - 1)

\frac{3}{4} - 1 = - \frac{1}{4}

= - \frac{1}{4} ln (7)

ln (\frac{s - 2}{s - 1})

x (ln (x^{3}) + ln (e x))

4 lo g_{10} (x) + 8 lo g_{10} (y)

7 + lo g_{10} (\frac{0.35}{1.7})

- lo g_{10} (1.8 \cdot 1 0^{- 13})