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Popular >

simplify 4ln(3)+ln(2^6)

Solution

simplify

4 ln (3) + ln (2^{6})

Solution

2 ln (72)

+1

Decimal Notation

8.55333 \dots

Solution steps

4 ln (3) + ln (2^{6})

Apply log rule:

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

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

= ln (3^{4}) + ln (2^{6})

Apply log rule:

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

ln (3^{4}) + ln (2^{6}) = ln (2^{6} \cdot 3^{4})

= ln (2^{6} \cdot 3^{4})

3^{4} \cdot 2^{6} = 5184

= ln (5184)

Rewrite

5184

in power-base form:

5184 = 7 2^{2}

= ln (7 2^{2})

Apply log rule:

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

ln (7 2^{2}) = 2 ln (72)

= 2 ln (72)

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Frequently Asked Questions (FAQ)

What is 4ln(3)+ln(2^6) ?
The solution to 4ln(3)+ln(2^6) is 2ln(72)