What is ln(3/2)-ln(7)+ln(5) ?

The solution to ln(3/2)-ln(7)+ln(5) is ln(15/14)

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simplify ln(3/2)-ln(7)+ln(5)

simplify

ln (\frac{3}{2}) - ln (7) + ln (5)

ln (\frac{15}{14})

Decimal Notation

0.06899 \dots

Solution steps

ln (\frac{3}{2}) - ln (7) + ln (5)

Apply log rule:

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

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

= ln (\frac{\frac{3}{2}}{7}) + ln (5)

\frac{\frac{3}{2}}{7} = \frac{3}{14}

= ln (\frac{3}{14}) + ln (5)

Apply log rule:

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

ln (\frac{3}{14}) + ln (5) = ln (5 \cdot \frac{3}{14})

= ln (5 \cdot \frac{3}{14})

\frac{3}{14} \cdot 5 = \frac{15}{14}

= ln (\frac{15}{14})

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