What is ln(18)+ln(7)-ln(20) ?

The solution to ln(18)+ln(7)-ln(20) is ln(63/10)

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simplify ln(18)+ln(7)-ln(20)

simplify

ln (18) + ln (7) - ln (20)

ln (\frac{63}{10})

Decimal Notation

1.84054 \dots

Solution steps

ln (18) + ln (7) - ln (20)

Apply log rule:

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

ln (18) + ln (7) = ln (18 \cdot 7)

= ln (18 \cdot 7) - ln (20)

Multiply the numbers:

18 \cdot 7 = 126

= ln (126) - ln (20)

Apply log rule:

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

ln (126) - ln (20) = ln (\frac{126}{20})

= ln (\frac{126}{20})

Cancel the common factor:

2

= ln (\frac{63}{10})

lo g_{10} (\frac{y ^{5}}{3 x})

\frac{0.025693}{1} ln (\frac{1}{1.75 \cdot 1 0 ^{- 10}})

ln (\frac{3}{2 x ^{2} y})

lo g_{10} (\frac{x ^{6} y ^{9}}{z ^{2}})

- \frac{1}{4} ln (\frac{17}{34})