3^x + 25 = 26.2² + 3⁰

To solve the equation 3^x + 25 = 26.2^2 + 3^0, we can simplify the right side of the equation first.

3^0 = 1 (any number raised to the power of 0 is equal to 1)
26.2^2 = 26.2 * 26.2 = 686.44

Now, the equation becomes:

3^x + 25 = 686.44 + 1

Simplifying further:

3^x + 25 = 687.44

Subtracting 25 from both sides of the equation:

3^x = 687.44 - 25
3^x = 662.44

To solve for x, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) for this example:

ln(3^x) = ln(662.44)

Using the logarithmic property, we can bring down the exponent:

x * ln(3) = ln(662.44)

Now, divide both sides of the equation by ln(3):

x = ln(662.44) / ln(3)

Using a calculator, we can find the approximate value of x:

x ≈ 4.173