Logarithmic Transformations

Determine the transformations for the function below:

 $f\left(x\right)=-\log\left(2x+1\right)-3$  

• Reflect over x, Horizontal Stretch by 2, Left 1, Down 3

• Reflect over x, Horizontal Compress by 2, Left 1, Down 3

• Reflect over x, Horizontal Compress by 2, Right 1, Down 3

• Reflect over x, Horizontal Stretch by 2, Right 1, Down 3

Determine the transformations for the function below:

= $f\left(x\right)=2\log_2\left(x-4\right)$  

• Vertical Stretch by 2, Horizontal Compress by 2, Right 4

• Vertical Stretch by 2, Left 4

• Vertical Compress by 2, Right 4

• Vertical Stretch by 2, Right 4

Determine the transformations for the following:

 $f\left(x\right)=-\frac{1}{2}\log\left(\frac{2}{3}x\right)+2$  

• Reflect over x,  Vertical Compress by ½, Horizontal Stretch by ⅔, Up 2

• Reflect over x, Vertical Compress by ½, Horizontal Compress by ⅔, Up 2

• Vertical Compress by -½, Horizontal Stretch by ⅔, Up 2

• Reflect over x, Vertical Compress by ½, Horizontal Stretch by ⅔, Right 2

Determine the transformations for the following:

 $f\left(x\right)=\log_5\left(5x-4\right)-9$  

• Horizontal Stretch by 5, Right 4, Up 9

• Horizontal Compress by 5, Left 4, Down 9

• Horizontal Stretch by 5, Right 4, Down 9

• Horizontal Compress by 5, Right 4, Down 9

Determine the following transformations:

 $f\left(x\right)=2\log\left(x\right)$  

• Horizontal Compress by 2

• Horizontal Stretch by 2

• Vertical Stretch by 2

• Vertical Compress by 2

Solve the following: $2\log\left(x+1\right)=\log_3\left(2x-1\right)$  

• (23.654, 1.123)

• (1, 0)

• (1.865, 0.914)

• No Solution

Solve the following:

 $\log_2\left(x\right)=2\ln\left(8x-1\right)$  

• (0, 7.391)

• (0.158, -2.6617)

• (13.663, 2.456)

• No Solution

Solve the following:

 $2\log_5\left(3x+9\right)-10=\log\left(x+12\right)$  

• (-11, 0)

• (0, 1.079)

• (0, -7.27)

• No Solution