Let $$ b=\log k $$. Write the following expression in terms of $$ b $$. Assume $$ k0 $$. $$ \log (1000 k)= $$

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Let $$ b=\log k $$. Write the following expression in terms of $$ b $$. Assume $$ k>0 $$. $$ \log (1000 k)= $$

UpStudy AI · Accepted Answer

We start with the given expression  
$$
\log (1000k).
$$

Using the logarithm property for products, we have  
$$
\log (1000k)=\log(1000)+\log k.
$$

Since it is given that  
$$
b=\log k,
$$
we substitute to obtain  
$$
\log (1000k)= \log(1000) + b.
$$

Thus, the expression in terms of $$ b $$ is  
$$
\log (1000k)=\log(1000)+b.
$$

If the logarithm is base 10, note that  
$$
\log(1000)=\log(10^3)=3,
$$
and the expression simplifies to  
$$
\log (1000k)=3+b.
$$
The expression $$ \log (1000k) $$ in terms of $$ b $$ is $$ 3 + b $$.

Let \( b=\log k \). Write the following expression in terms of \( b \). Assume \( k>0 \). \( \log (1000 k)= \)

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