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Popular >

simplify 1/2 ln(36)+2ln(4)-ln(4)

Solution

simplify

\frac{1}{2} ln (36) + 2 ln (4) - ln (4)

Solution

ln (24)

+1

Decimal Notation

3.17805 \dots

Solution steps

\frac{1}{2} ln (36) + 2 ln (4) - ln (4)

Apply log rule:

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

\frac{1}{2} ln (36) = ln (3 6^{\frac{1}{2}})

= ln (3 6^{\frac{1}{2}}) + 2 ln (4) - ln (4)

Apply log rule:

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

2 ln (4) = ln (4^{2})

= ln (3 6^{\frac{1}{2}}) + ln (4^{2}) - ln (4)

Apply log rule:

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

ln (3 6^{\frac{1}{2}}) + ln (4^{2}) = ln (4^{2} \cdot 3 6^{\frac{1}{2}})

= ln (4^{2} \cdot 3 6^{\frac{1}{2}}) - ln (4)

3 6^{\frac{1}{2}} \cdot 4^{2} = 96

= ln (96) - ln (4)

Apply log rule:

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

ln (96) - ln (4) = ln (\frac{96}{4})

= ln (\frac{96}{4})

Divide the numbers:

\frac{96}{4} = 24

= ln (24)

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Frequently Asked Questions (FAQ)

What is 1/2 ln(36)+2ln(4)-ln(4) ?
The solution to 1/2 ln(36)+2ln(4)-ln(4) is ln(24)