Find the solution of the exponential equation

7+(5^5x)=25
correct to at least four decimal places.

To solve the exponential equation 7 + 5^(5x) = 25, we need to isolate the exponential term on one side of the equation. Here's how you can approach it:

Step 1: Subtract 7 from both sides of the equation:
7 + 5^(5x) - 7 = 25 - 7
5^(5x) = 18

Step 2: Take the logarithm of both sides of the equation. Since the base is not specified, we can use the common logarithm (log base 10) or the natural logarithm (ln, log base e). I'll use the natural logarithm (ln) here:
ln(5^(5x)) = ln(18)

Step 3: Use the logarithmic property to bring the exponent down:
(5x)ln(5) = ln(18)

Step 4: Divide both sides of the equation by ln(5) to solve for 5x:
5x = ln(18) / ln(5)

Step 5: Divide both sides of the equation by 5 to solve for x:
x = (ln(18) / ln(5)) / 5

Now let's calculate the value of x using a calculator to the desired decimal places:

Calculating ln(18) and ln(5):
ln(18) ≈ 2.8903718
ln(5) ≈ 1.6094379

Dividing ln(18) by ln(5):
ln(18) / ln(5) ≈ 1.7968106

Dividing by 5 to find x:
x ≈ 1.7968106 / 5 ≈ 0.3593621

So, the solution to the exponential equation 7 + 5^(5x) = 25, correct to at least four decimal places, is x ≈ 0.3594.