Mathematics

This is a logarithmic transformation problem. The key insight is that the range of a logarithm depends on what values the argument (the input to the log) can take. Since $\log_7$ can output any real number as its argument ranges over all positive values, you need to figure out what $x+5$ can be, then see what $\log_7(x+5)$ produces, and finally account for the vertical shift of $+2$. The domain restriction on $x$ will constrain the argument, which in turn determines the range.

This is a logarithmic transformation problem. The key insight is that the range of a logarithm depends on what values the argument (the input to the log) can take. Since $\log_7$ can output any real number as its argument ranges over all positive values, you need to figure out what $x+5$ can be, then see what $\log_7(x+5)$ produces, and finally account for the vertical shift of $+2$. The domain restriction on $x$ will constrain the argument, which in turn determines the range.