Question

suppose that ln 2 = a and ln 5 = b. use properties of logarithm in terms of a and b.
ln ^7√20
my answer choices are
a) (1/7)(a^2+b)
b) (1/7)(2a+b)
c) (2/7)(a-b)
d) (2/7)(a+b)

Answer 1

\[\ln \sqrt[7]{20} = \ln 20^{1/7} = \frac{1}{7}\ln 20 \]
\[=\frac{1}{7}\ln (4*5) = \frac{1}{7}(\ln 4 + \ln 5) = \frac{1}{7}(\ln 2^{2} + \ln 5) = \frac{1}{7}(2\ln 2 + \ln 5)\]
\[=\frac{1}{7}(2a + b)\]