Maths problem:how to do, thanks?

(◕‿◕✿)　新年進步

The x-intercept is 3, so when x = 3, y = 0, then we have 0 = a + log_b (3) ...[1]
The curve passes through (81, 3), so we have 3 = a + log_b (81) ...[2]

Consider [2] - [1]:
3 = log_b (81) - log_b (3)
3 = log_b (3⁴) - log_b (3)
3 = 4 log_b (3) - log_b (3)
3 = 3 log_b (3)
log_b (3) = 1
b = 3

Put back to [1], 0 = a + log₃ (3) = a + 1, so a = -1.

Therefore,
y = -1 + log₃(x)
log₃(x) = y + 1
x = 3^(y + 1)