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

Let's break it down! We start with the expression \( \log (1000 k) \). Using the properties of logarithms, we can separate this into two parts: \[ \log (1000 k) = \log 1000 + \log k \] Now, we know \( \log 1000 = \log (10^3) = 3 \) since \( 1000 = 10^3 \). Given that \( b = \log k \), we can substitute that into our expression: \[ \log (1000 k) = 3 + \log k = 3 + b \] So, in terms of \( b \), we express \( \log (1000 k) \) as: \[ \log (1000 k) = 3 + b \]