Question 487640
log x + log 2x = log 50
log x + log 2x - log 50=0
place under a single log using log rules of multiplication and division
log(x*2x/50)=0
Convert to exponential form: base(10) raised to log of number(0)=number (x*2x/50)
10^0=(x*2x/50)
1=2x^2/50
2x^2=50
x^2=50/2=25
x=±√25=±5
x=-5 (reject, x>0)
or
x=5 (ans)
Check:
log x + log 2x = log 50
log 5+log10=log 5*10=log 50