Questions: Rewrite each of the following equations: (a) Rewrite 2^4=16 as a logarithmic equation: (b) Rewrite log 0.0001=-4 as an exponential equation:

Transcript text: Rewrite each of the following equations: (a) Rewrite $2^{4}=16$ as a logarithmic equation: $\square$ (b) Rewrite $\log 0.0001=-4$ as an exponential equation: $\square$

Solution

Solution Steps

Step 1: Rewrite $2^{4}=16$ as a logarithmic equation

The exponential equation $2^{4}=16$ can be rewritten in logarithmic form using the definition of logarithms:
If $a^{b}=c$, then $\log_{a}c = b$.
Applying this to $2^{4}=16$, we get:
$\log_{2}16 = 4$.

Step 2: Rewrite $\log 0.0001=-4$ as an exponential equation

The logarithmic equation $\log 0.0001=-4$ can be rewritten in exponential form using the definition of logarithms:
If $\log_{a}c = b$, then $a^{b}=c$.
Here, the base $a$ is $10$ (since no base is specified, it is assumed to be $10$).
Applying this to $\log 0.0001=-4$, we get:
$10^{-4}=0.0001$.

Final Answer

(a) $ \boxed{\log_{2}16 = 4} $
(b) $ \boxed{10^{-4} = 0.0001} $

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