What is the missing number in this simplified exponential expression: 7^(?)-:7^(5)=7^(12) ?
(1 point)
The missing number is 17.
To solve for the missing number, we can use the properties of exponents. We know that dividing two exponential expressions with the same base is equivalent to subtracting their exponents.
So, the equation can be rewritten as:
7^(?) - 7^(5) = 7^(12)
To solve for the missing number, let's first isolate the term with the missing exponent.
7^(?) = 7^(12) + 7^(5)
Now, to find the value of the missing exponent, we can take the logarithm of both sides of the equation.
log(7^(?)) = log(7^(12) + 7^(5))
Using the properties of logarithms, we can simplify the equation further. The logarithm of an exponential expression with the same base is equal to the exponent.
? * log(7) = log(7^(12) + 7^(5))
Now, we can substitute the values into the equation to find the missing exponent.
? * log(7) = log(7^(12) + 7^(5))
? * log(7) = log(7^(12)) + log(7^(5))
Using the property of logarithms that states log(a^b) = b * log(a), we can further simplify.
? * log(7) = 12 * log(7) + 5 * log(7)
We can divide both sides of the equation by log(7) to isolate the missing exponent.
? = (12 * log(7) + 5 * log(7)) / log(7)
? = (12 + 5)
? = 17
Therefore, the missing number in the simplified exponential expression is 17.
To find the missing number in this simplified exponential expression, we can use the property of exponentiation which states that subtracting exponents is the same as dividing the base.
Given: 7^(?)-:7^(5)=7^(12)
To solve for the missing number, we need to rearrange the equation by moving the terms around:
7^(?) = 7^(12) + 7^(5)
Next, we can combine the terms on the right side of the equation by adding the exponents, since the base is the same (7).
7^(?) = 7^(12 + 5)
7^(?) = 7^(17)
Now, to solve for the missing number, we need to determine what exponent (power) of 7 will result in 7 raised to that exponent being equal to 7^(17).
Therefore, the missing number in the exponential expression is 17.
To find the missing number in this exponential expression, we need to use the rules of exponents.
The given equation is: 7^? - 7^5 = 7^12.
To simplify this equation, we'll apply the rule that states that when we subtract two exponential expressions with the same base, we can divide the larger exponent by the smaller exponent.
So, dividing 7^? by 7^5, we get: 7^? ÷ 7^5 = 7^(12-5).
Now, we can simplify the left side of the equation to 7^(?-5) = 7^7.
Therefore, the value of ?-5 is equal to 7.
Adding 5 to both sides of the equation, we find that ? = 7 + 5 = 12.
So, the missing number in the simplified exponential expression is 12.