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Popular >

simplify 2ln(3)+ln(4)

Solution

simplify

2 ln (3) + ln (4)

Solution

2 ln (6)

+1

Decimal Notation

3.58351 \dots

Solution steps

2 ln (3) + ln (4)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} \cdot 4 = 36

= ln (36)

Rewrite

36

in power-base form:

36 = 6^{2}

= ln (6^{2})

Apply log rule:

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

ln (6^{2}) = 2 ln (6)

= 2 ln (6)

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Frequently Asked Questions (FAQ)

What is 2ln(3)+ln(4) ?
The solution to 2ln(3)+ln(4) is 2ln(6)