log (little 3) X + log (little6) X = 2

Question

the answer is 3.9

can anyone please explain how do you get this answer? Thank you

Answer 1

log₃ x + log₆x = 2

we can change bases by
loglog_a b = log b/log a , (base 10)

so your equation is
logx/log3 + logx/log6 = 2
logx(1/log3 + 1/log6) = 2
logx = 2/(1/log3 + 1/log6) = .59154 appr.
x = 10^.59154 = 3.904