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Popular >

simplify ln(9)+3ln(4)

Solution

simplify

ln (9) + 3 ln (4)

Solution

2 ln (24)

+1

Decimal Notation

6.35610 \dots

Solution steps

ln (9) + 3 ln (4)

Apply log rule:

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

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

= ln (9) + ln (4^{3})

Apply log rule:

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

ln (9) + ln (4^{3}) = ln (4^{3} \cdot 9)

= ln (4^{3} \cdot 9)

9 \cdot 4^{3} = 576

= ln (576)

Rewrite

576

in power-base form:

576 = 2 4^{2}

= ln (2 4^{2})

Apply log rule:

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

ln (2 4^{2}) = 2 ln (24)

= 2 ln (24)

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Frequently Asked Questions (FAQ)

What is ln(9)+3ln(4) ?
The solution to ln(9)+3ln(4) is 2ln(24)