What is ln((\sqrt[7]{\frac{5(2)^3)/(3^2)}}{6^2}) ?

The solution to ln((\sqrt[7]{\frac{5(2)^3)/(3^2)}}{6^2}) is 1/7 ln(40/9)-2ln(6)

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simplify ln((\sqrt[7]{\frac{5(2)^3)/(3^2)}}{6^2})

simplify

\frac{1}{7} ln (\frac{40}{9}) - 2 ln (6)

Decimal Notation

- 3.37042 \dots

Solution steps

Apply log rule:

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

Apply log rule:

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

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

= \frac{1}{7} ln (\frac{2 ^{3} \cdot 5}{3 ^{2}}) - 2 ln (6)

\frac{5 \cdot 2 ^{3}}{3 ^{2}} = \frac{40}{9}

= \frac{1}{7} ln (\frac{40}{9}) - 2 ln (6)

2 lo g_{8} (z - 6) - 4 lo g_{8} (z + 2)

ln (\frac{0.472 \cdot 1490}{0.406})

ln (x - 2) + ln (8)

ln (8) - ln (- 1)

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

What is ln((\sqrt[7]{\frac{5(2)^3)/(3^2)}}{6^2}) ?
The solution to ln((\sqrt[7]{\frac{5(2)^3)/(3^2)}}{6^2}) is 1/7 ln(40/9)-2ln(6)