Question 863308
If assumed you can make a graph of {{{y=log(2,x)}}}, it appears like:
{{{graph(300,300,-15,15,-15,15,log(2,x))}}}


{{{f(x)=log(2,x+1)-2}}} is <b>1 unit shifted to the left and 2 units shifted downward</b>.



Just a bit more help.
Before the shift, vertical asymptote x=0.  After the shift, it is at x=-1.
Can you figure the axis intercepts?  For y-intercept, x=0.  Set the equation that way and solve for y.