How can I figure out the x in this one without calculator? 5^(2x) = 5^(2) * 5^(x)
You have to choose a number that when multiplied by itself will equal the same number when added to itself. There is only one number that will do that: 2. So 2 x 2=4 and 2 + 2=4. Because, the left hand side you would multiply: 2 * x, while the right hand side you would add the exponents: 2 + x. So, 2 is the only answer. There are "complex" answers, but that is probably beyond your understanding.
