Question

Rewrite as a logarithmic equation.
** See picture attached

Answer 1

`- 5 \log 2 = - \log 32`

Explanation:

We have to convert an exponential equation into the logarithmic equation.

The given equation is

`2^(-5) = (1)/(32)`

Now, taking log on both sides we get,

`\log 2^(-5) = \log(1)/(32)`

⇒
`- 5 \log 2 = \log 1 - \log 32`

{Since we know from the logarithmic property that
`\log a^(b) = b \log a` and
`\log (a)/(b) = \log a - \log b` }

⇒
`- 5 \log 2 = - \log 32` {Since
`\log 1 = 0` }

Hence, this is the required logarithmic equation. (Answer)