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Popular >

simplify ln(72)-2ln(3)

Solution

simplify

ln (72) - 2 ln (3)

Solution

3 ln (2)

+1

Decimal Notation

2.07944 \dots

Solution steps

ln (72) - 2 ln (3)

Apply log rule:

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

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

= ln (72) - ln (3^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (72) - ln (3^{2}) = ln (\frac{72}{3 ^{2}})

= ln (\frac{72}{3 ^{2}})

\frac{72}{3 ^{2}} = 8

= ln (8)

Rewrite

8

in power-base form:

8 = 2^{3}

= ln (2^{3})

Apply log rule:

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

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

= 3 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(72)-2ln(3) ?
The solution to ln(72)-2ln(3) is 3ln(2)