Question

to solve the equation \\(2^{x-1} - 7 = 9\\), first add 7 to each side.

what common base can be used to rewrite each side of the resulting equation?

• 2
• 4
• 16
• 32

which is the equation of \\(2^{x-1} - 7 = 9\\) after it is reduced so that both sides of the equation are exponential functions with the same base?

• \\(2^{x-1} = 4^2\\)
• \\(2^{x-1} - 7^1 = 3^2\\)
• \\(2^{x-1} - 7 = 3^2\\)
• \\(2^{x-1} = 2^4\\)

Explanation:

Isolate the exponential term

Using the Solving Exponential Equations Algebraically knowledge point

$$
LATEXBLOCK0
$$

Identify the common base

Using the Solving Exponential Equations Algebraically knowledge point

$$
LATEXBLOCK1
$$

Rewrite with the same base

Using the Solving Exponential Equations Algebraically knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question 1

To solve the equation \(2^{x-1} - 7 = 9\), first <blank>add 7 to each side</blank>.

Question 2

What common base can be used to rewrite each side of the resulting equation?

• 2 (Correct answer)
• 4
• 16
• 32

Question 3

Which is the equation of \(2^{x-1} - 7 = 9\) after it is reduced so that both sides of the equation are exponential functions with the same base?

• \(2^{x-1} = 4^2\)
• \(2^{x-1} - 7^1 = 3^2\)
• \(2^{x-1} - 7 = 3^2\)
• \(2^{x-1} = 2^4\) (Correct answer)