To solve an equation, we perform the inverse operation. What does inverse mean?
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Assuming you meant <span>e⁴ thus
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![\bf ln\left( \sqrt[7]{e^4} \right)\implies log_e\left( e^{\frac{4}{7}} \right)\\\\ -----------------------------\\\\ log_{{ a}}{{ a}}^x\implies x=x\impliedby \textit{let's use this cancellation rule}\\\\ -----------------------------\\\\ log_e\left( e^{\frac{4}{7}} \right)\iff \cfrac{4}{7}](https://tex.z-dn.net/?f=%5Cbf%20ln%5Cleft%28%20%5Csqrt%5B7%5D%7Be%5E4%7D%20%5Cright%29%5Cimplies%20log_e%5Cleft%28%20e%5E%7B%5Cfrac%7B4%7D%7B7%7D%7D%20%5Cright%29%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0Alog_%7B%7B%20%20a%7D%7D%7B%7B%20%20a%7D%7D%5Ex%5Cimplies%20x%3Dx%5Cimpliedby%20%5Ctextit%7Blet%27s%20use%20this%20cancellation%20rule%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0Alog_e%5Cleft%28%20e%5E%7B%5Cfrac%7B4%7D%7B7%7D%7D%20%5Cright%29%5Ciff%20%5Ccfrac%7B4%7D%7B7%7D)
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We choose the coordinates (4,4), (4,10), and (8,4) as the vertices of right-angle triangle ABC
We want to dilate triangle ABC by scale factor of 2 at the center (0,2)
The image is shown below as triangle A'B'C' with coordinates (8.6), (8,18), and (18,6).
Triangle ABC has a base of 4 units and a height of 6 units
Triangle A'B'C' has a base of 8 units and a height of 12 units
Applying Pythagoras theorem to triangle ABC to find the hypotenuse
Now, we calculate the hypotenuse of the image
The hypotenuse of the image is twice the hypotenuse of triangle ABC which proof the two shapes are similar shape
We want to dilate triangle ABC by scale factor of 2 at the center (0,2)
The image is shown below as triangle A'B'C' with coordinates (8.6), (8,18), and (18,6).
Triangle ABC has a base of 4 units and a height of 6 units
Triangle A'B'C' has a base of 8 units and a height of 12 units
Applying Pythagoras theorem to triangle ABC to find the hypotenuse
Now, we calculate the hypotenuse of the image
The hypotenuse of the image is twice the hypotenuse of triangle ABC which proof the two shapes are similar shape