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

Answer 1

To solve the equation 5^x ÷ 5^5 = 5^12, we can use the property of exponents that states: a^m ÷ a^n = a^(m-n).

Applying this property, we have:
5^x ÷ 5^5 = 5^12
By subtracting the exponents, we can rewrite the equation as:
5^(x-5) = 5^12

For the equation to be true, the exponent on both sides must be equal. Therefore, we have:
x - 5 = 12

Adding 5 to both sides, we find:
x = 17

Therefore, the value of x to make the exponential equation true is 17.