Using the Quotient Rule of Exponents, what is the exponent in an equivalent form of 7976 if the base is 7

Answer 1

The Quotient Rule of Exponents states that when dividing two numbers with the same base, you subtract the exponents.

In this case, we have 7976 as the base raised to some exponent. We want to find the exponent in an equivalent form when the base is 7.

Let's say the exponent we are looking for is "x". Using the Quotient Rule of Exponents, we can set up the following equation:

7^x = 7976

To solve for x, we need to take the logarithm of both sides of the equation. Using the natural logarithm (ln) as an example, we have:

ln(7^x) = ln(7976)

Using the logarithmic property that ln(a^b) = b * ln(a), we can simplify the left side:

x * ln(7) = ln(7976)

Now, to solve for x, we divide both sides of the equation by ln(7):

x = ln(7976) / ln(7)

Using a calculator, we can find the approximate value of x to be approximately 5.439.

Therefore, the exponent in an equivalent form of 7976 when the base is 7 is approximately 5.439.