Answer:
Exact solution to the equation is 10-log4(x+6) = 9 is -2
Explanation:
As we have given the logarithm equation in the question that
[tex]10-log4(x+6)=9[/tex] ……….(1)
Now by using the logarithm property, we know that
x+6>0
So x>-6
Now from equation 1
[tex]log4(x+6)=1[/tex]
As we know the anti log property as [tex]loga(x)=b[/tex] then it becomes [tex](x)=(a)^b[/tex]
Now by using anti log Properties, the above equation would becomes
[tex]x+6=(4)^1[/tex]
[tex]x+6=(4)[/tex]
[tex]x=-6+(4)[/tex]
So x=-2
Hence the possible value of x that satisfy the given logarithm equation is -2.
