Question

What is the y-intercept of the function y = log4 (2x+64) +3?

Answer 1

(0, 6)

Explanation:

Given function:

`y=\log_4(2x+64)+3`

The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.

Therefore, to find the y-intercept, substitute x = 0 into the function:

`\implies y=\log_4(2(0)+64)+3`

`\implies y=\log_4(64)+3`

Rewrite 64 as 4³:

`\implies y=\log_4(4)^3+3`

`\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax`

`\implies y=3\log_4(4)+3`

`\textsf{Apply log law}: \quad \log_aa=1`

`\implies y=3(1)+3`

`\implies y=3+3`

`\implies y=6`

Therefore, the y-intercept of the given function is (0, 6).