Question
4^log16 (7)
the base of the log is 16. 4 is being raised to the entire log16 (7).
show all steps please!
the base of the log is 16. 4 is being raised to the entire log16 (7).
show all steps please!
Answers
Reiny
4^log<sub>16</sub> 7
= (16^(1/2))^log<sub>16</sub> 7
= (16)^((1/2))^log<sub>16</sub> 7)
= 16^log<sub>16</sub> sqrt(7)
recall the property that
a^log<sub>a</sub> k = k
16^log<sub>16</sub> sqrt(7)
= sqrt(7)
or , using your calculator
4^log<sub>16</sub> 7
= 4^(log7/log16)
= 4^.70183873
= 2.645751309 and sqrt(7) = 2.645751311
not bad
= (16^(1/2))^log<sub>16</sub> 7
= (16)^((1/2))^log<sub>16</sub> 7)
= 16^log<sub>16</sub> sqrt(7)
recall the property that
a^log<sub>a</sub> k = k
16^log<sub>16</sub> sqrt(7)
= sqrt(7)
or , using your calculator
4^log<sub>16</sub> 7
= 4^(log7/log16)
= 4^.70183873
= 2.645751309 and sqrt(7) = 2.645751311
not bad