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Popular >

simplify 3ln(3)-3ln(1/2)

Solution

simplify

3 ln (3) - 3 ln (\frac{1}{2})

Solution

3 ln (6)

+1

Decimal Notation

5.37527 \dots

Solution steps

3 ln (3) - 3 ln (\frac{1}{2})

Apply log rule:

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

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

= ln (3^{3}) - 3 ln (\frac{1}{2})

Apply log rule:

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

3 ln (\frac{1}{2}) = ln ((\frac{1}{2})^{3})

= ln (3^{3}) - ln ((\frac{1}{2})^{3})

Apply log rule:

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

ln (3^{3}) - ln ((\frac{1}{2})^{3}) = ln (\frac{3 ^{3}}{( \frac{1}{2} ) ^{3}})

= ln (\frac{3 ^{3}}{( \frac{1}{2} ) ^{3}})

\frac{3 ^{3}}{( \frac{1}{2} ) ^{3}} = 216

= ln (216)

Rewrite

216

in power-base form:

216 = 6^{3}

= ln (6^{3})

Apply log rule:

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

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

= 3 ln (6)

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Frequently Asked Questions (FAQ)

What is 3ln(3)-3ln(1/2) ?
The solution to 3ln(3)-3ln(1/2) is 3ln(6)