What is ln(7)-ln(14)+ln(10) ?

The solution to ln(7)-ln(14)+ln(10) is ln(5)

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simplify ln(7)-ln(14)+ln(10)

simplify

ln (7) - ln (14) + ln (10)

ln (5)

Decimal Notation

1.60943 \dots

Solution steps

ln (7) - ln (14) + ln (10)

Apply log rule:

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

ln (7) - ln (14) = ln (\frac{7}{14})

= ln (\frac{7}{14}) + ln (10)

Cancel the common factor:

7

= ln (\frac{1}{2}) + ln (10)

Apply log rule:

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

ln (\frac{1}{2}) + ln (10) = ln (10 \cdot \frac{1}{2})

= ln (10 \cdot \frac{1}{2})

\frac{1}{2} \cdot 10 = 5

= ln (5)

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

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ln (\frac{e ^{x}}{2})

2 ln (x + 1) - 2 ln (x) + 4 ln (3 x + 1)