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Popular >

simplify ln(9)+2ln(2)

Solution

simplify

ln (9) + 2 ln (2)

Solution

2 ln (6)

+1

Decimal Notation

3.58351 \dots

Solution steps

ln (9) + 2 ln (2)

Apply log rule:

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

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

= ln (9) + ln (2^{2})

Apply log rule:

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

ln (9) + ln (2^{2}) = ln (2^{2} \cdot 9)

= ln (2^{2} \cdot 9)

9 \cdot 2^{2} = 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 ln(9)+2ln(2) ?
The solution to ln(9)+2ln(2) is 2ln(6)