Answer:
[tex]x=-0.792[/tex]
Step-by-step explanation:
We are given the equation,
[tex]16^{x}+9=0[/tex]
i.e. [tex]16^{x}=-9[/tex]
Applying log on both the sides, we get, [tex]\log(16^{x})=-\log(9)[/tex]
Now, using the properties of log given by [tex]\log(b^{x})=x \log{b}[/tex].
We get, [tex]x \log(16)=\log(9^{-1})[/tex]
i.e. [tex]x \log(16)=\log(\frac{1}{9})[/tex]
i.e. [tex]x=\log(\frac{\log(1/9)}{\log(16)})[/tex]
i.e. [tex]x=\frac{-0.954}{1.204}[/tex]
i.e. [tex]x=-0.792[/tex]
Hence, the solution of [tex]16^{x}+9=0[/tex] is [tex]x=-0.792[/tex].
