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Popular >

simplify ln(9)+4ln(2)

Solution

simplify

ln (9) + 4 ln (2)

Solution

2 ln (12)

+1

Decimal Notation

4.96981 \dots

Solution steps

ln (9) + 4 ln (2)

Apply log rule:

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

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

= ln (9) + ln (2^{4})

Apply log rule:

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

ln (9) + ln (2^{4}) = ln (2^{4} \cdot 9)

= ln (2^{4} \cdot 9)

9 \cdot 2^{4} = 144

= ln (144)

Rewrite

144

in power-base form:

144 = 1 2^{2}

= ln (1 2^{2})

Apply log rule:

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

ln (1 2^{2}) = 2 ln (12)

= 2 ln (12)

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Frequently Asked Questions (FAQ)

What is ln(9)+4ln(2) ?
The solution to ln(9)+4ln(2) is 2ln(12)