Question

log5 (x+2)- log5 10=log5 100 how do you solve this

Answer 1

(log(x+2))/(log(5))-(log(10))/(log(5)) = (log(100))/(log(5))
Add (log(10))/(log(5)) to both sides:
(log(x+2))/(log(5)) = (log(10))/(log(5))+(log(100))/(log(5))
Divide both sides by 1/(log(5)):
log(x+2) = log(5) ((log(10))/(log(5))+(log(100))/(log(5)))
Cancel logarithms by taking exp of both sides:
x+2 = 1000
Subtract 2 from both sides:
x = 998
Now test that this solution is appropriate by substitution into the original equation:
Check the solution x = 998:
(log(x+2))/(log(5))-(log(10))/(log(5)) => -(log(10))/(log(5))+(log(2+998))/(log(5)) = (2 log(2)+2 log(5))/(log(5)) ~~ 2.86135
(log(100))/(log(5)) => (log(100))/(log(5)) = (log(100))/(log(5)) ~~ 2.86135
So the solution is correct.
Thus, the solution is:
x = 998

Answer 2

log(ab)=loga + logb
using this formula for your problem :
log5+ log(x+2)-log5-log10=log5+log100
now individually put values of log5, log10 , log 100 , and then take anti log of x+2
There might be some other easier way ,but as per now , I could recall this much only.

Answer 3

Solution posted by @DHASHNI is absolutely correct and shortcut too. Go for it ! :-)