What is ln(8)+ln(6)-ln(12) ?

The solution to ln(8)+ln(6)-ln(12) is 2ln(2)

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simplify ln(8)+ln(6)-ln(12)

simplify

ln (8) + ln (6) - ln (12)

2 ln (2)

Decimal Notation

1.38629 \dots

Solution steps

ln (8) + ln (6) - ln (12)

Apply log rule:

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

ln (8) + ln (6) = ln (8 \cdot 6)

= ln (8 \cdot 6) - ln (12)

Multiply the numbers:

8 \cdot 6 = 48

= ln (48) - ln (12)

Apply log rule:

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

ln (48) - ln (12) = ln (\frac{48}{12})

= ln (\frac{48}{12})

Divide the numbers:

\frac{48}{12} = 4

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{2}) = 2 ln (2)

= 2 ln (2)

ln (\frac{x ^{2}}{y ^{5}})

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lo g_{10} (\frac{17 x}{y})