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# Describe the changes to the graph of `y = log_4 x` when x is replaced by `16x^2`

lkballer24 | Student, Grade 11 | Valedictorian

Posted June 6, 2013 at 10:51 PM via web

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Describe the changes to the graph of `y = log_4 x` when x is replaced by `16x^2`

Tagged with logarithm, math, transformation

### 1 Answer |

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 7, 2013 at 2:15 AM (Answer #1)

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Describe the changes to `y=log_4 x` when x is replaced by `16x^2` :

`y=log_4 16x^2`

Use the log property `log(ab)=loga+logb`

`y=log_4 16+log_4 x^2`

Use the log property `log(a^n)=nloga`

`y=log_4 16+2log_4 x`

Note that `log_4 16=2` since `4^2=16`

`y=2+2log_4 x`

Since we are adding 2 the graph is translated (shifted) up 2 units. Since we are multiplying by 2 the graph is stretched vertically by a factor of 2.

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The transformations are a vertical stretch of factor two followed by a translation up two units.

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The graphs:

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