SOLUTION: The question reads: Express the following in terms of ln 5 and ln 7. a) ln(1/125) b)ln 9.8 c) ln 7sqrt7 d) ln 1225 e)ln .056 f)(ln 35 + ln(1/7))/(ln 25) I'm sure its reall

Question 155147This question is from textbook University Calculus
: The question reads: Express the following in terms of ln 5 and ln 7.
a) ln(1/125)
b)ln 9.8
c) ln 7sqrt7
d) ln 1225
e)ln .056
f)(ln 35 + ln(1/7))/(ln 25)
I'm sure its really easy i just dont know why i cant figure it out... thanks for the helpThis question is from textbook University Calculus

Answer by stanbon(48535) (Show Source):
You can put this solution on YOUR website!
Express the following in terms of ln 5 and ln 7.
a) ln(1/125) = ln(5^-3) = -3ln(5)
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b)ln 9.8 = ?
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c) ln 7sqrt7 = ln(7) + (1/2)ln(7) = (3/2)ln(7)
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d) ln 1225 = ln(5^2*7^2) = 2ln(5) + 2ln(7)
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e)ln .056 = ?
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f)(ln 35 + ln(1/7))/(ln 25)
= (ln(5*7) + ln(7^-1)) / ln(5^2)
= (ln(5) + ln(7) - ln(7)) / 2ln(5)
= (ln(5))/(2ln(5))
= 1/2
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Cheers,
Stan H.