Question

0.90^60x=A^xFind the value of A that makes the following equafion true for all values of x

Answer 1

The value of A that makes the equation true is;

`A=0.9^(60)`

Step-by-step explanation:

We want to find the value of A that will make the equation below true;

`0.9^(60x)=A^x`

Using the laws of indices we ca re-write the equation as;

`(0.9^(60))^x=A^x`

Then finding the xth root of both sides, we have;

`\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}`

Therefore, the value of A that makes the equation true is;

`A=0.9^(60)`