Question

While solving for x, 3*5^(8x)=573. Step 1, you should:

Answer 1

The solution for
`\(x\)` is approximately
`\(0.285\)`.

To solve the equation
`\(3 \cdot 5^(8x) = 573\)` for
`\(x\)`, follow these steps:

1. Divide both sides of the equation by 3:

`\[5^(8x) = (573)/(3)\]`

Simplify the right side:

`\[5^(8x) = 191\]`

2. Take the logarithm (base 5) of both sides:

`\[8x = \log_5(191)\]`

3. Solve for
`\(x\)`:

`\[x = (\log_5(191))/(8)\]`

Now, use a calculator to find the numerical value for
`\(x\)`:

`\[x \approx (\log_5(191))/(8) \approx (2.278753601)/(8) \approx 0.2848442001\]`

Therefore, the solution for
`\(x\)` is approximately
`\(0.285\)`.

The question probable may be:

"Find the value of x in the equation:
`3 * 5^((8x)) = 573` "