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Popular >

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

Solution

simplify

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

Solution

3 ln (12)

+1

Decimal Notation

7.45471 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{3} \cdot 2^{6} = 1728

= ln (1728)

Rewrite

1728

in power-base form:

1728 = 1 2^{3}

= ln (1 2^{3})

Apply log rule:

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

ln (1 2^{3}) = 3 ln (12)

= 3 ln (12)

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Frequently Asked Questions (FAQ)

What is 3ln(3)+ln(2^6) ?
The solution to 3ln(3)+ln(2^6) is 3ln(12)