What is simplify-(ln(5/4)-ln(7)+ln(5))/2 ?

The solution to simplify-(ln(5/4)-ln(7)+ln(5))/2 is -(ln(25/28))/2

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simplify-(ln(5/4)-ln(7)+ln(5))/2

simplify

- \frac{ln ( \frac{5}{4} ) - ln ( 7 ) + ln ( 5 )}{2}

- \frac{ln ( \frac{25}{28} )}{2}

Decimal Notation

0.05666 \dots

Solution steps

- \frac{ln ( \frac{5}{4} ) - ln ( 7 ) + ln ( 5 )}{2}

Apply log rule:

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

ln (\frac{5}{4}) - ln (7) = ln (\frac{\frac{5}{4}}{7})

= - \frac{ln ( 5 ) + ln ( \frac{\frac{5}{4}}{7} )}{2}

\frac{\frac{5}{4}}{7} = \frac{5}{28}

= - \frac{ln ( \frac{5}{28} ) + ln ( 5 )}{2}

Apply log rule:

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

ln (\frac{5}{28}) + ln (5) = ln (5 \cdot \frac{5}{28})

= - \frac{ln ( 5 \cdot \frac{5}{28} )}{2}

\frac{5}{28} \cdot 5 = \frac{25}{28}

= - \frac{ln ( \frac{25}{28} )}{2}

2 C - ln (- x^{2} + 1^{\frac{1}{2}} - y^{2} + 1^{\frac{1}{2}})

3 (ln (3) - ln (x)) + (ln (x) - ln (9))

ln (2 - 5) - ln (e^{2} + e^{4} + 1)

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

ln ∣ x ∣ - ln x^{2}

What is simplify-(ln(5/4)-ln(7)+ln(5))/2 ?
The solution to simplify-(ln(5/4)-ln(7)+ln(5))/2 is -(ln(25/28))/2