Question

What is x if `log_3(x) +log_2(x+6)=3`?

Answer 1

`1.18" "` approx

Explanation:

In general`" " log_b a" can be written as " loga/logb`

`log_3(x)+log_2(x+6)=3" can be written as " logx/log3+log (x+6)/log2=3`

`log2*logx+log3*log (x+6)=3log2*log3`

`logx^log2=log8^log3-log (x+6)^log3`

`logx^log2=log (8/(x+6))^log3`

Antilog both sides...

`x^log2=(8/(x+6))^log3`

I guess, it can be solved by graphing...