Find the value of x to make this exponential equation true… 5^x ÷ 5^5 = 5^12

Answer 1

To solve this exponential equation, we can use the properties of exponents.

First, let's simplify both sides of the equation.
On the left side, we have 5^x ÷ 5^5. According to the rule a^m ÷ a^n = a^(m-n), we can subtract the exponents when dividing the same base. Therefore, 5^x ÷ 5^5 = 5^(x-5).

Now, our equation is 5^(x-5) = 5^12.

To make the exponents the same on both sides, we can set (x-5) equal to 12.

Therefore, x - 5 = 12.

To isolate x, we add 5 to both sides of the equation:
x = 12 + 5.

Thus, the value of x that makes the exponential equation true is x = 17.