The Quotient Rule of Logarithms Quick Check
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Using numerical analysis and the Power Rule of Logarithms, log x^k = k log x, how can log (1/100) be rewritten? (1 point)
Responses
10 log−2
10 logarithm negative 2
−2 log 10
negative 2 logarithm 10
2 log−10
2 logarithm negative 10
log−20
and this
Using numerical analysis and the Quotient Rule of Logarithms, how can log 11 (14/t) be rewritten? (1 point)
Responses
log 11 (14−t)
logarithm subscript 11 baseline left parenthesis 14 minus t right parenthesis
log 11 14 + log 11 t
logarithm subscript 11 baseline 14 plus logarithm subscript 11 baseline t
log 11 t−log 11 14
logarithm subscript 11 baseline t minus logarithm subscript 11 baseline 14
log 11 14−log 11 t
and this
Using numerical analysis and the Quotient Rule of Logarithms, how can log (r^3/n^2) be rewritten?(1 point)
Responses
3 log r−2 log n
3 logarithm r minus 2 logarithm n
2 log n−3 log r
2 logarithm n minus 3 logarithm r
3 log r+2 log n
3 logarithm r plus 2 logarithm n
3 log r/2 log n
and this
Using the properties log b(1/m) =−log b m and log b(m/n) = log b m−log b n, how can ln 11−3 ln p be condensed? (1 point)
Responses
ln (11−p^3)
l n left parenthesis 11 minus p cubed right parenthesis
ln (11−3p)
l n left parenthesis 11 minus 3 p right parenthesis
ln (11/3p)
l n left parenthesis Start Fraction 11 over 3 p End Fraction right parenthesis
ln (11/p^3)
and this
Using the Quotient Rule of Logarithms, the Product Rule of Logarithms, and the Power Rule of Logarithms, how can log(x^2/5y) be fully expanded?(1 point)
Responses
log x−log 5−log y
logarithm x minus logarithm 5 minus logarithm y
2 log x−log 5−log y
2 logarithm x minus logarithm 5 minus logarithm y
log x^2−log (5y)
logarithm x squared minus logarithm left parenthesis 5 y right parenthesis
2 log x−log (5y)
2 logarithm x minus logarithm left parenthesis 5 y right parenthesis
what are the correct answers for all 5 questions?
For the first question, using the Power Rule of Logarithms, log (1/100) can be rewritten as -2 log 10.
For the second question, using the Quotient Rule of Logarithms, log 11 (14/t) can be rewritten as log 11 14 - log 11 t.
For the third question, using the Quotient Rule of Logarithms, log (r^3/n^2) can be rewritten as 3 log r - 2 log n.
For the fourth question, using the properties log b(1/m) = -log b m and log b(m/n) = log b m - log b n, ln 11 - 3 ln p can be condensed as ln (11/p^3).
For the fifth question, using the Product Rule of Logarithms, the Quotient Rule of Logarithms, and the Power Rule of Logarithms, log(x^2/5y) can be fully expanded as 2 log x - log 5 - log y.
So, the correct answers are:
1) -2 log 10
2) log 11 14 - log 11 t
3) 3 log r - 2 log n
4) ln (11/p^3)
5) 2 log x - log 5 - log y