$$ 1 \leftarrow $$ Check the Integer Values box and change the window setting to $$ [-10,10] imes[-10,10] $$. Use the sliders to graph function $$ f(x)=6 \log _{4}(x-2)-3 $$. What is the equation of the vertical asymptote? Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. The vertical asymptote is described by the equation (Type an equation.)

Question

$$ 1 \leftarrow $$ Check the Integer Values box and change the window setting to $$ [-10,10] 	imes[-10,10] $$. Use the sliders to graph function $$ f(x)=6 \log _{4}(x-2)-3 $$. What is the equation of the vertical asymptote? Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. The vertical asymptote is described by the equation (Type an equation.)

UpStudy AI · Accepted Answer

1. The given function is  
   $$
   f(x)=6 \log_{4}(x-2)-3.
   $$

2. The vertical asymptote for a logarithmic function occurs when the argument of the logarithm is zero. Set the argument equal to zero:
   $$
   x-2=0.
   $$

3. Solve for $$ x $$:
   $$
   x=2.
   $$

4. Therefore, the vertical asymptote is given by the equation  
   $$
   x=2.
   $$
The vertical asymptote is $$ x = 2 $$.

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