Answer:
[tex]- 5 \log 2 = - \log 32[/tex]
Step-by-step explanation:
We have to convert an exponential equation into the logarithmic equation.
The given equation is
[tex]2^{-5} = \frac{1}{32}[/tex]
Now, taking log on both sides we get,
[tex]\log 2^{-5} = \log\frac{1}{32}[/tex]
⇒ [tex]- 5 \log 2 = \log 1 - \log 32[/tex]
{Since we know from the logarithmic property that [tex]\log a^{b} = b \log a[/tex] and [tex]\log \frac{a}{b} = \log a - \log b[/tex] }
⇒ [tex]- 5 \log 2 = - \log 32[/tex] {Since [tex]\log 1 = 0[/tex] }
Hence, this is the required logarithmic equation. (Answer)
