Answer:
The value of A that makes the equation true is;
[tex]A=0.9^{60}[/tex]
Explanation:
We want to find the value of A that will make the equation below true;
[tex]0.9^{60x}=A^x[/tex]
Using the laws of indices we ca re-write the equation as;
[tex](0.9^{60})^x=A^x[/tex]
Then finding the xth root of both sides, we have;
[tex]\begin{gathered} (0.9^{60})^x=A^x \\ \sqrt[x]{(0.9^{60})^x}=\sqrt[x]{A^x} \\ 0.9^{60}=A \\ A=0.9^{60} \end{gathered}[/tex]
Therefore, the value of A that makes the equation true is;
[tex]A=0.9^{60}[/tex]
