Algebra Log Equation Problem, help w/ steps?

Posted on 2016-05-04 18:38:00 in Math by PHEEL

Can you please show me the steps of how to solve algebraically, both approximate and exact solution to 3 decimal places: 

(will be base 10) 
log8x-log((1+(x^1/2)) = 2 

book says solution is: [(725+125(33^1/2)]/8 = ~~~180.384 


I've tried a number of various starting formats of this and have yet to get the correct solution. Any tips would be helpful. 
Also could you show the steps for this one as well, though I dont have the solution: 

(again common log, base 10) 

log4x-log([(12 +( (x)^1/2)]= 2 

I suspect its same steps, so I will practice on this one once I learn the method for the above problem. Which is why I would greatly appreciate the steps for this solution as well.

Update: I'd be interested to see any and all the possible ways to arrive via precalculus algebra to the correct solution. This is more because I am curious to see and enjoy that aspect of math. I wouldn't expect it, since it may be a lot of work, but if you do have the time - it would not be taken for granted.

---

Answer Comment

No Answers Posted Yet.