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 help This question is from textbook University Calculus

Answer by stanbon(75887) (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)
--------------------------------------
b)ln 9.8 = ?
--------------------------------------
c) ln 7sqrt7 = ln(7) + (1/2)ln(7) = (3/2)ln(7)
--------------------------------------
d) ln 1225 = ln(5^2*7^2) = 2ln(5) + 2ln(7)
--------------------------------------
e)ln .056 = ?
--------------------------------------
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
===============
Cheers,
Stan H.

RELATED QUESTIONS
Write as a single logarithm and check with a calculator a) ln 5 + ln 3 b) ln 2+ ln 10... (answered by jim_thompson5910,stanbon)

Solve the exponential equation. Express the solution set in terms of natural logarithms. (answered by LinnW)

Express the following logarithms in terms of ln 2 and ln 3. 1) ln... (answered by Edwin McCravy)

Which equation is equivalent to y=7x^5 A. Ln(y) = ln (7) + 5 ln (x) B. Y = ln (7) + 5... (answered by Alan3354)

How do you use log laws to write ln 8 + ln 125 - ln 40 in the terms of ln... (answered by nerdybill)

express log in terms of ln 5 and ln 7 ln (1/25) (answered by Alan3354)

Solve the exponential equation. Express the solution set in terms of natural logarithms: (answered by stanbon)

Write the logarithm in terms of ln 5 and ln 9. ln (5/9) (answered by Alan3354)

log6 (3) + log5 (2) is equivalent to A 0 B ln(2) * ln (6) C 1 / ln(6) D ln(2) / ln (answered by rapaljer)