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Popular >

simplify ln(9)+4ln(4)

Solution

simplify

ln (9) + 4 ln (4)

Solution

2 ln (48)

+1

Decimal Notation

7.74240 \dots

Solution steps

ln (9) + 4 ln (4)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

9 \cdot 4^{4} = 2304

= ln (2304)

Rewrite

2304

in power-base form:

2304 = 4 8^{2}

= ln (4 8^{2})

Apply log rule:

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

ln (4 8^{2}) = 2 ln (48)

= 2 ln (48)

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Frequently Asked Questions (FAQ)

What is ln(9)+4ln(4) ?
The solution to ln(9)+4ln(4) is 2ln(48)