It is given that
[tex] log2x + logx =2 [/tex]
Using [tex] loga+logb = log(ab)[/tex]
We get, [tex] log(2x^2) = 2 [/tex]
Also, if [tex] loga = b [/tex] . Then [tex] a=antilog(b) [/tex]
Therefore, [tex] 2x^2 = antilog(2) [/tex]
[tex] 2x^2 = 100[/tex]
Dibide both sides by 2
[tex] x^2 = 50 [/tex]
[tex] x= \sqrt50 [/tex]
[tex] x = 7.0711 [/tex] is the required answer.
Given equation is [tex]\log(2x)+\log(x)=2[/tex]
Now we have to solve this equation using properties of logs.
[tex]\log(2x)+\log(x)=2[/tex]
Apply formula
[tex]\log(A)+\log(B)=\log(A*B)[/tex]
[tex]\log(2x*x)=2[/tex]
[tex]\log(2x^2)=2[/tex]
convert into exponent form using formula
[tex]\log(a)=b => 10^b=a[/tex]
[tex]2x^2=10^2[/tex]
[tex]2x^2=100[/tex]
[tex]x^2=\frac{100}{2}[/tex]
[tex]x^2=50[/tex]
take square root of both sides
x=7.0710678118
Rounding to nearest thousandth gives final answer as x=7.071
