AnswersAdvanced Algebra Concepts and ConnectionsSolving Logarithmic Equations Using Technology

Solving Logarithmic Equations Using Technology — Quiz Answers

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1
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Which is equivalent to the log base 2 of n is equal to 4 ?

A
n is equal to the fraction with numerator log 2 and denominator log 4
B
log n is equal to 4 log 2
C
n is equal to log 4 times log 2
D
log n is equal to the fraction with numerator log 2 and denominator 4
2
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Which system of equations could be graphed to solve the equation? the log of open paren 2 x plus 1 close paren is equal to 3 x minus 2

A
y sub 1 is equal to 3 x , y sub 2 is equal to 2 x
B
y sub 1 is equal to the log of open paren 2 x plus 1 plus 2 close paren , y sub 2 is equal to 3 x
C
y sub 1 is equal to the log of open paren 2 x plus 1 close paren , y sub 2 is equal to 3 x minus 2
D
y sub 1 is equal to log 2 plus 1 , y sub 2 is equal to 3 x minus 2
3

A teacher used the change of base formula to determine whether the equation is correct. open paren the log base 2 of 10 close paren times open paren the log base 4 of 8 close paren times open paren the log base 10 of 4 close paren is equal to 3 Which statement explains whether the equation is correct?

A
The equation is correct since open paren the log base 2 of 10 close paren times open paren the log base 4 of 8 close paren times open paren the log base 10 of 4 close paren is equal to log times open paren 2 times 10 close paren times log times open paren 4 times 8 close paren times log times open paren 10 times 4 close paren is equal to log times 20 times log times 32 times log times 40 is equal to 3
B
The equation is not correct since open paren the log base 2 of 10 close paren times open paren the log base 4 of 8 close paren times open paren the log base 10 of 4 close paren is equal to log times 10 halves times log times 8 fourths times log 4 tenths is equal to log 5 times log times 2 times log 0 point 4 is equal to negative 0 point 0 8
C
The equation is correct since open paren the log base 2 of 10 close paren times open paren the log base 4 of 8 close paren times open paren the log base 10 of 4 close paren is equal to the fraction with numerator log 10 and denominator log 2 times the fraction with numerator log 8 and denominator log 4 times the fraction with numerator log 4 and denominator log 10 is equal to the fraction with numerator log 8 and denominator log 2 is equal to 3
D
The equation is not correct since open paren the log base 2 of 10 close paren times open paren the log base 4 of 8 close paren times open paren the log base 10 of 4 close paren is equal to the fraction with numerator log 10 and denominator log 2 times the fraction with numerator log 8 and denominator log 4 times the fraction with numerator log 4 and denominator log 10 is equal to the fraction with numerator log 8 and denominator log 2 is equal to 4
4

Which expression results when the change of base formula is applied to log sub 4 of open paren x plus 2 close paren ?

A
the fraction with numerator log 4 and denominator the log of open paren x plus 2 close paren
B
the fraction with numerator log 4 and denominator log x plus 2
C
the fraction with numerator log x plus 2 and denominator log 4
D
the fraction with numerator the log of open paren x plus 2 close paren and denominator log 4
5

Devonte used the change of base formula to approximate the log base 8 of 25 Which expression did Devonte use?

A
log 25 eighths
B
the fraction with numerator log 8 and denominator log 25
C
the fraction with numerator log 25 and denominator log 8
D
the log of 8 over 25
6

What is the approximate value of x in the equation? the log base 3 fourths of 25 is equal to 3 x minus 1

A
0 point 9 5 5
B
0 point 3 0 4
C
negative 0 point 7 0 8
D
negative 3 point 3 9 6
7

What is the approximate value of q in the equation? q plus the log base 2 of 6 is equal to 2 q plus 2

A
3 point 0 7 9
B
negative 1 point 5 2 2
C
negative 1 point 6 1 3
D
0 point 5 8 5
9

Which expression can be used to approximate the expression, for all positive numbers A , b , and x , where A is not equal to 1 and b is not equal to 1 ? the log base A of x

A
the fraction with numerator the log base A of b and denominator the log base x of b
B
the fraction with numerator the log base b of x and denominator the log base b of A
C
the fraction with numerator the log base b of A and denominator the log base b of x
D
the fraction with numerator the log base A of x and denominator the log base b of x
10

What is the approximate value of x in the equation? the log base 5 of 15 is equal to x plus 3

A
2 point 8 8 0
B
negative 2 point 5 2 3
C
negative 1 point 3 1 7
D
7 point 4 8 5

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