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Popular >

simplify ln(3^4*2^6)

Solution

simplify

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

Solution

4 ln (3) + 6 ln (2)

+1

Decimal Notation

8.55333 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (2^{6}) = 6 ln (2)

= 4 ln (3) + 6 ln (2)

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Frequently Asked Questions (FAQ)

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