What is ln(9/7)*500/6 ?

The solution to ln(9/7)*500/6 is (250(2ln(3)-ln(7)))/3

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simplify ln(9/7)*500/6

simplify

ln (\frac{9}{7}) \cdot \frac{500}{6}

\frac{250 ( 2 ln ( 3 ) - ln ( 7 ) )}{3}

Decimal Notation

20.94286 \dots

Solution steps

ln (\frac{9}{7}) \frac{500}{6}

Apply log rule:

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

ln (\frac{9}{7}) = ln (9) - ln (7)

= \frac{500}{6} (ln (9) - ln (7))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{500 ( ln ( 9 ) - ln ( 7 ) )}{6}

Cancel the common factor:

2

= \frac{250 ( ln ( 9 ) - ln ( 7 ) )}{3}

ln (9) = 2 ln (3)

= \frac{250 ( 2 ln ( 3 ) - ln ( 7 ) )}{3}

3 lo g_{b} (x) - 6 lo g_{b} (z) - 4 lo g_{b} (w)

4 + 2 lo g_{5} (x) - \frac{1}{3} lo g_{5} (y)

- ln (\frac{2 l + d}{l}) + ln (\frac{l + d}{l}) + ln (\frac{l + d}{d})

- lo g_{10} (7.93 \cdot 1 0^{- 3})

\frac{2}{7} lo g_{10} (a) - \frac{1}{8} lo g_{10} (b)