Question

Evaluate 6^(log14/log6)

Answer 1

any guesses for this one?

Answer 2

I used log rules but I didn't get the right answer. I tried to go log base of 6 with 0= log14/log6 as well.

Answer 3

by definition
\[b^x=e^{x\log(b)}\] so
\[6^{\frac{\log(14)}{\log(6)}}\]
\[=e^\frac{\log(14)}{\log(6)\times \log(6)}\]
\[=e^{\log(14)}=14\]

Answer 4

ok i made a typo on line 3 above

Answer 5

thanks, 14 is the right answer!

Answer 6

\[e^{\frac{\log(14)}{\log(6)}\log(6)}=e^{\log(14)}=14\]

Answer 7

yw, sorry about the typo