Question 251254
{{{y = log(4, (x)) + 4}}}
Since the logarithm is base 4 ans since no calculator I know can find base 4 logarithms, it will help tremendously if we choose our x values wisely. We want to choose x's that are powers of 4! For the three x's greater than 1: 4, 16 and 64 (since {{{4 = 4^1}}}, {{{16 = 4^2}}} and {{{64 = 4^3}}}). For the x's between 0 an 1: 1/4, 1/16 and 1/64 (since {{{1/4 = 4^(-1)}}}, {{{1/16 = 4^(-2)}}} and {{{1/64 = 4^(-3)}}}. And even x = 1 is a power of 4 since {{{1 = 4^0}}}!<br>
Using these x's we get:
x = 4: {{{y = log(4, (4)) + 4 = 1 + 4 = 5}}}
x = 16: {{{y = log(4, (16)) + 4 = 2 + 4 = 6}}}
x = 64: {{{y = log(4, (64)) + 4 = 3 + 4 = 7}}}
x = 1/4: {{{y = log(4, (1/4)) + 4 = -1 + 4 = 3}}}
x = 1/16: {{{y = log(4, (1/16)) + 4 = -2 + 4 = 2}}}
x = 1/64: {{{y = log(4, (1/64)) + 4 = -3 + 4 = 1}}}
x = 1: {{{y = log(4, (1)) + 4 = 0 + 4 = 4}}}
We now have 7 points to plot.<br>
The asymptotes for a logarithmic equation will be vertical asymptotes at values for x that make an argument of a logarithm zero, if any. We have just one logarithm so we find the asymptotes, if any, by setting the argument equal to zero and solving:
x = 0
(Not much solving to do here!) There is a vertical asymptote at x = 0 (aka the y-axis).