What is the missing number in this simplified exponential expression: 7^(?)-:7^(5)=7^(12) ?

Question

(1 point)

Answer 1

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.