SOLUTION: For each of the following equations either prove that it is correct (by using the rules of logarithms and exponents) or else show that it is not correct (by finding numerical value

Question 32682: For each of the following equations either prove that it is correct (by using the rules of logarithms and exponents) or else show that it is not correct (by finding numerical values for the variables that make the values of the two sides of the equation different).
log (x/y) = log x/ log y
log x - log y = log (x/y)
log (2x) = 2 log x
2 log x = log (x^2)
log x+1 / x+3 = log (x+1) - log (x+3)
log (x square root x^2 + 1) = log x + 1/2 (x^2 +1)
log (x^2 +1) = 2 log x + log 1
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
For each of the following equations either prove that it is correct (by using the rules of logarithms and exponents) or else show that it is not correct (by finding numerical values for the variables that make the values of the two sides of the equation different).
log (x/y) = log x/ log y
LHS....LOG(10/1)=LOG(10)=1...BUT RHS... LOG(10)/LOG(10)=1/0.....NOT CORRECT
log x - log y = log (x/y)
OK..AS PER FORMULA..
log (2x) = 2 log x
LHS.....LOG(2*1)=LOG(2).....RHS....2*LOG(1)=2*0=0....NOT CORRECT
2 log x = log (x^2)
CORRECT AS PER FORMULA LOG(X)^N=N*LOG(X)
log {(x+1) / (x+3)} = log (x+1) - log (x+3)...I SUPPOSE THIS IS THE PROBLEM.
CORRECT AS PER FORMULA...LOG(A/B)=LOG(A)-LOG(B)
log {(x *square root (x^2 + 1)} = log x + 1/2 (x^2 +1)
WRONG...LHS....LOG{1*SQRT(1^2+1)}=LOG{SQRT(2)}
RHS......LOG(1)+(1/2)*(1+1)=0+1=1...WHICH IS NOT CORRECT.
log (x^2 +1) = 2 log x + log 1
WRONG...LHS.....LOG(1^2+1)=LOG(2)
RHS.....2*LOG(1)+LOG(1)=0+0=0.......WHICH IS NOT CORRECT...
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