Question

3logx(6)+4logx(6)=10

Answer 1

First 3log_x(6) = log_x(6^3) and 4log_x(6) = log_x(6^4).

So 3logx(6)+4logx(6) = log_x(6^3) + log_x(6^4)
= log_x(6^3 . 6^4)
= log_x(6^7)

Hence if 3logx(6)+4logx(6)=10 then log_x(6^7) = 10

Or in other words, 6^7 = x^10. I.e., x = 6^(7/10) = ....

Answer 2

http://www.wolframalpha.com/input/?i=solve%283logx%286%29%2B4logx%286%29%3D10%2Cx%29

Answer 3

@Hero: Actually no -- you've transcribed the equation into Wolfram incorrectly. The x here is not the argument of the log function, but its base.