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Popular >

simplify ln(4)+3ln(3)-ln(12)

Solution

simplify

ln (4) + 3 ln (3) - ln (12)

Solution

2 ln (3)

+1

Decimal Notation

2.19722 \dots

Solution steps

ln (4) + 3 ln (3) - ln (12)

Apply log rule:

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

3 ln (3) = ln (3^{3})

= ln (4) + ln (3^{3}) - ln (12)

Apply log rule:

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

ln (4) + ln (3^{3}) = ln (3^{3} \cdot 4)

= ln (3^{3} \cdot 4) - ln (12)

4 \cdot 3^{3} = 108

= ln (108) - ln (12)

Apply log rule:

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

ln (108) - ln (12) = ln (\frac{108}{12})

= ln (\frac{108}{12})

Divide the numbers:

\frac{108}{12} = 9

= ln (9)

Rewrite

9

in power-base form:

9 = 3^{2}

= ln (3^{2})

Apply log rule:

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

ln (3^{2}) = 2 ln (3)

= 2 ln (3)

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lo g_{10} (x^{2}) y^{3}

expand log_{b}((x^2y)/(z^5))expand

lo g_{b} (\frac{x ^{2} y}{z ^{5}})

Frequently Asked Questions (FAQ)

What is ln(4)+3ln(3)-ln(12) ?
The solution to ln(4)+3ln(3)-ln(12) is 2ln(3)