Question

When is `g(x)=0` for the function `g(x)=5*2^(3x)+4`?

Answer 1

If `g(x)=5 * 2^(3x)+4`
then `g(x)` is never `=0`

Explanation:

For any positive value `k` and any Real value `p`
`color(white)("XXX")k^p > 0`

Therefore
`color(white)("XXX")2^(3x) > 0` for `AAx in RR`

and
`color(white)("XXX")rarr 5*2^(3x) > 0` for `AAx in RR`

and
`color(white)("XXX")rarr 5*2(3x)+4 > 0` for `AAx in RR`

Answer 2

For this function, `g(x) != 0`.

Explanation:

This is an exponential function, and, generally, exponential functions have no `y`-value equal to `0`. This is because no exponent of any number will give you `0` (or anything smaller than it).

The only way to have an exponential function which intercepts the `x`-axis is the translate the graph downwards.