I am tackling a problem as below:
$F(x)=\ln x$. The graph is transformed into a function $g$ by a translation of $(3 , -2)$, followed by a reflection in the $x$-axis. Find an expression for $g$, giving your answer as a single logarithm.
My thoughts are here:
After the transformation: $$g(x)=-\ln(x+3)-2$$ Then I tried to make it into a single logarithm: $$g(x)=-(\ln x+\ln 3)-2=-\ln3x-2$$
How can I change the digit 2 also into a logarithm form?? Help!
First of all, your $g(x)$ isn't correct; it should be $-\ln(x-3)+2$. Now write $2=\ln e^2$, and the answer follows: $$-\ln(x-3)+\ln e^2=\ln\frac{e^2}{x-3}$$