Determine the equation of the line that represents the vertical f(x)=log_(4)(x+4)+5

The given function is \( f(x) = \log_{4}(x+4) + 5 \).<br /><br />To find the vertical asymptote of this logarithmic function, we need to determine where the argument of the logarithm becomes zero. The argument of the logarithm is \( x + 4 \). Setting it equal to zero gives:<br /><br />\[ x + 4 = 0 \]<br /><br />Solving for \( x \), we get:<br /><br />\[ x = -4 \]<br /><br />Therefore, the equation of the vertical asymptote is \( x = -4 \).