Math  /  Algebra

QuestionSuppose that ln2=a\ln 2=\mathrm{a} and ln5=b\ln 5=\mathrm{b}. Use properties of logarithms to write the loga terms of aa and bb.
In 207\sqrt[7]{20} A. 27(ab)\frac{2}{7}(a-b) B. 17(2a+b)\frac{1}{7}(2 a+b) C. 17(a2+b)\frac{1}{7}\left(a^{2}+b\right) D. 27(a+b)\frac{2}{7}(a+b)

Studdy Solution
Substitute back into the expression for ln207\ln \sqrt[7]{20}:
ln207=17ln20=17(2a+b)\ln \sqrt[7]{20} = \frac{1}{7} \ln 20 = \frac{1}{7}(2a + b)
The expression that matches one of the given options is:
17(2a+b) \boxed{\frac{1}{7}(2a + b)}

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