The equation \( y=\log (x+3) \) has a vertical asymptote at: \( x=\square \)

The equation \( y = \log(x + 3) \) has a vertical asymptote where the argument of the logarithm function is zero. To find this point, set \( x + 3 = 0 \), which gives \( x = -3 \). Therefore, as \( x \) approaches \(-3\) from the right, the logarithm tends to negative infinity, confirming the vertical asymptote at \( x = -3 \). Another interesting aspect is how the logarithmic function behaves as \( x \) increases. As \( x \) goes towards infinity, \( y = \log(x + 3) \) will increase without bound, reflecting how logarithmic growth is slower than linear but continues indefinitely. This makes logarithmic functions quite fascinating in various fields, particularly in modeling phenomena like population growth or sound intensity levels!