SOLUTION: log10e5+log10(5x+1)=log10(x+5)+1 find x

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Question 930565: log10e5+log10(5x+1)=log10(x+5)+1 find x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if you have this:
log%2810%2Ce%5E5%29%2Blog%2810%2C%285x%2B1%29%29=log%2810%2C%28x%2B5%29%29%2B1 then x will be:

log%2810%2Ce%5E5%285x%2B1%29%29=log%2810%2C10%28x%2B5%29%29 ...since log same,
e%5E5%285x%2B1%29=10%28x%2B5%29 is same too
e%5E5%285x%2B1%29=10%28x%2B5%29
5xe%5E5%2Be%5E5=10x%2B50
5xe%5E5-10x=50-e%5E5
%285e%5E5-10%29x=50-e%5E5
x=-%28e%5E5-50%29%2F%285e%5E5-10%29
x+=+-%28e%5E5-50%29%2F5%28e%5E5-2%29........exact solution
or,you can substitute => e%5E5=148.4 and get approximate solution

148.4%285x%2B1%29=10%28x%2B5%29
742x%2B148.4=10x%2B50
742x-10x=50-148.4
732x=-98.4
x=-98.4%2F732
x=-0.1344262295081967%29

if you plug in this solution in log%2810%2Ce%5E5%29%2Blog%2810%2C%285x%2B1%29%29=log%2810%2C%28x%2B5%29%29%2B1 and you check it, you will get 1.687172570169473=1.68713406159622243 which could be rounded to 1.6871=1.6871 to be same (error is to small)