Question

What are the solutions 16^+ 9=0

Answer 1

`x=-0.792`

Explanation:

We are given the equation,

`16^(x)+9=0`

i.e.
`16^(x)=-9`

Applying log on both the sides, we get,
`\log(16^(x))=-\log(9)`

Now, using the properties of log given by
`\log(b^(x))=x \log{b}`.

We get,
`x \log(16)=\log(9^(-1))`

i.e.
`x \log(16)=\log((1)/(9))`

i.e.
`x=\log((\log(1/9))/(\log(16)))`

i.e.
`x=(-0.954)/(1.204)`

i.e.
`x=-0.792`

Hence, the solution of
`16^(x)+9=0` is
`x=-0.792`.