Solving Logarithmic Equations Using Technology — Quiz
Question 3 • Mathematics III
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?
Answer
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