Given that ${{3}^{x}}={{2}^{kx}}$ for all values of $x$, find $k$, giving your answer in terms of na

Question

Given that ${{3}^{x}}={{2}^{kx}}$ for all values of $x$, find $k$, giving your answer in terms of natural logarithms. Describe a geometrical transformation which maps the graph of $y={{2}^{x}}$ onto the graph of $y={{3}^{x}}$.

Accepted Answer

$k=\dfrac{\ln3}{\ln2}$. Stretch parallel to the $x$-axis by scale factor $\dfrac{\ln2}{\ln3}$

ACJC Tutorial 3 Question 10

ACJC Tutorial 3 Question 10

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