Find the value of x to make this exponential equation true… 5^x ÷ 5^5 = 5^12
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.
To solve the exponential equation 5^x ÷ 5^5 = 5^12, we can use the laws of exponents. According to the law of division, when we divide two exponential expressions with the same base, the exponents are subtracted. Thus, we have:
5^x ÷ 5^5 = 5^12
Since the bases are the same (which is 5), we can simplify the equation to:
5^(x-5) = 5^12
Now, since the bases are the same, the exponents must be equal. Therefore, we equate the exponents:
x - 5 = 12
To isolate the variable x, we add 5 to both sides of the equation:
x = 12 + 5
Simplifying further:
x = 17
Hence, the value of x that makes the exponential equation true is x = 17.
To find the value of x that makes the equation 5^x ÷ 5^5 = 5^12 true, we will use the property of exponents that states when dividing two exponentiated terms with the same base, you subtract the exponents.
In this case, we have 5^x ÷ 5^5 = 5^12. Since the base is 5 for all terms, we can subtract the exponents:
x - 5 = 12.
To isolate x, we can add 5 to both sides of the equation:
x = 12 + 5.
Therefore, x = 17.
The value of x that makes the equation true is 17.