4^log16 (7)

Question

the base of the log is 16. 4 is being raised to the entire log16 (7).

show all steps please!

Answer 1

4^log₁₆ 7
= (16^(1/2))^log₁₆ 7
= (16)^((1/2))^log₁₆ 7)
= 16^log₁₆ sqrt(7)

recall the property that
a^log_a k = k

16^log₁₆ sqrt(7)
= sqrt(7)

or , using your calculator
4^log₁₆ 7
= 4^(log7/log16)
= 4^.70183873
= 2.645751309 and sqrt(7) = 2.645751311
not bad