Sum-log

The sum of two numbers is 19, and the sum of their logarithms (base 10) is 1.6. Determine these numbers.

Final Answer:

x =  16.6021
y =  2.3979

Step-by-step explanation:

x+y= 19 log x + log y = 1.6  y = 19x  log xy = 1.6 xy = 10 1.6  x(19x) = 10 1.6  19 xx2101.6 = 0  x219x+39.81071705535=0  x219 x+39.81071705535=0 x219x+39.811=0  a=1;b=19;c=39.811 D=b24ac=1924139.811=201.7571317786 D>0  x1,2=2ab±D=219±201.76 x1,2=9.5±7.102062 x1=16.60206188 x2=2.39793812  x=x1=16.6021

Our quadratic equation calculator calculates it.

y=19x y=x2=2.39792.3979   Verifying Solution:   s1=x+y=16.6021+2.3979=19 s2=log10(x)+log10(y)=log1016.6021+log102.3979=58=153=1.6



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