Answer:
x = 3
Step-by-step explanation:
You want the equation of the vertical asymptote of the function h(x)=6log₂(x−3)−5.
Vertical asymptote
The vertical asymptote of the parent log function log(x) is x = 0. For the given function it will be located where the argument of the log function is zero:
x -3 = 0
x = 3
The equation of the vertical asymptote is x = 3.
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Additional comment
The leading coefficient (6) and the base (2) serve only as vertical scale factors of the log function. The added value -5 shifts the curve down 5 units, so has no effect on the vertical asymptote. The horizontal translation of the function right 3 units is what moves the asymptote away from x = 0.
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