Question

logarithms?

log (base 9) x+3 log (base 3) x=14

Answer 1

log9(x) = log3(x) * log9(3)
what is log9(3)
9^log9(3) = 3
9^.5 = 3
so
log 9(x) = .5 log3(x)
Now the problem
.5 log3(x) + 3 log3(x) = 14
log3 (x^.5) + log3(x^3) = 14
log 3 (x^3.5) = 14
x^3.5 = 3^14
now use plain old base ten logs
3.5 log x = 14 log 3
log x = 1.91
x = 10^1.91 = 81.3
Check my arithmetic!!!

Answer 2

deeeeeeeeez ntus