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Popular >

simplify 2ln(3)+4ln(2)-ln(36)

Solution

simplify

2 ln (3) + 4 ln (2) - ln (36)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

2 ln (3) + 4 ln (2) - ln (36)

Apply log rule:

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

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

= ln (3^{2}) + 4 ln (2) - ln (36)

Apply log rule:

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

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

= ln (3^{2}) + ln (2^{4}) - ln (36)

Apply log rule:

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

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

= ln (2^{4} \cdot 3^{2}) - ln (36)

3^{2} \cdot 2^{4} = 144

= ln (144) - ln (36)

Apply log rule:

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

ln (144) - ln (36) = ln (\frac{144}{36})

= ln (\frac{144}{36})

Divide the numbers:

\frac{144}{36} = 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)

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Frequently Asked Questions (FAQ)

What is 2ln(3)+4ln(2)-ln(36) ?
The solution to 2ln(3)+4ln(2)-ln(36) is 2ln(2)