What is ln(12)+1/2 ln(7)-ln(2) ?

The solution to ln(12)+1/2 ln(7)-ln(2) is ln(6*7^{1/2})

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simplify ln(12)+1/2 ln(7)-ln(2)

simplify

ln (12) + \frac{1}{2} ln (7) - ln (2)

ln (6 \cdot 7^{\frac{1}{2}})

Decimal Notation

2.76471 \dots

Solution steps

ln (12) + \frac{1}{2} ln (7) - ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (7) = ln (7^{\frac{1}{2}})

= ln (12) + ln (7^{\frac{1}{2}}) - ln (2)

Apply log rule:

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

ln (12) + ln (7^{\frac{1}{2}}) = ln (12 \cdot 7^{\frac{1}{2}})

= ln (12 \cdot 7^{\frac{1}{2}}) - ln (2)

Apply log rule:

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

ln (12 \cdot 7^{\frac{1}{2}}) - ln (2) = ln (\frac{12 \cdot 7 ^{\frac{1}{2}}}{2})

= ln (\frac{12 \cdot 7 ^{\frac{1}{2}}}{2})

Divide the numbers:

\frac{12}{2} = 6

= ln (6 \cdot 7^{\frac{1}{2}})

ln (- 2) - ln (- 5)

ln (- e^{- x} x)

ln (2) + ln (\frac{3}{2})

0.27 + 5 - 5 lo g_{10} (4.84 x 1 0^{- 6})

\frac{1}{100} ln (\frac{87.14}{101.3})

What is ln(12)+1/2 ln(7)-ln(2) ?
The solution to ln(12)+1/2 ln(7)-ln(2) is ln(6*7^{1/2})