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Popular >

simplify 4ln(1/3)-6ln(1/9)

Solution

simplify

4 ln (\frac{1}{3}) - 6 ln (\frac{1}{9})

Solution

8 ln (3)

+1

Decimal Notation

8.78889 \dots

Solution steps

4 ln (\frac{1}{3}) - 6 ln (\frac{1}{9})

Apply log rule:

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

4 ln (\frac{1}{3}) = ln ((\frac{1}{3})^{4})

= ln ((\frac{1}{3})^{4}) - 6 ln (\frac{1}{9})

Apply log rule:

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

6 ln (\frac{1}{9}) = ln ((\frac{1}{9})^{6})

= ln ((\frac{1}{3})^{4}) - ln ((\frac{1}{9})^{6})

Apply log rule:

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

ln ((\frac{1}{3})^{4}) - ln ((\frac{1}{9})^{6}) = ln (\frac{( \frac{1}{3} ) ^{4}}{( \frac{1}{9} ) ^{6}})

= ln (\frac{( \frac{1}{3} ) ^{4}}{( \frac{1}{9} ) ^{6}})

\frac{( \frac{1}{3} ) ^{4}}{( \frac{1}{9} ) ^{6}} = 6561

= ln (6561)

Rewrite

6561

in power-base form:

6561 = 3^{8}

= ln (3^{8})

Apply log rule:

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

ln (3^{8}) = 8 ln (3)

= 8 ln (3)

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Frequently Asked Questions (FAQ)

What is 4ln(1/3)-6ln(1/9) ?
The solution to 4ln(1/3)-6ln(1/9) is 8ln(3)