11. Solve for x in the equation [ 25^x-5^2 x-1=500 ( (smiks) ) ]

Question

Answer 1

To solve for

in the equation

, we can start by expressing both terms with the same base.First, note that

. Therefore, we can rewrite

as \( (5^2)^x = 5^{2x} \).Now, the equation becomes:

Next, factor out

from both terms:

Simplify the expression inside the parentheses:

Divide both sides by 4:

Now, express 125 as a power of 5:

So, we have:

Since the bases are the same, we can equate the exponents:

Solve for

:

Therefore, the solution to the equation is

.

Question