When solving the problem 7 ^ (x + 2) = 7 ^ (3x - 8) your fiend does the following 7(x) + 2 = 7(3x) - 8; 7x + 2 = 21x - 8; 10 = 14x; x = 5/7 Was this correct ? (1 point ) This is not correct When the bases are the same , then we can set the exponents equal to each other and solve that equation This is not correct . Both sides should be divided by 7 instead of multiplied by 7 Yes , this is correct No error was made This is not correct The 7 needs to be distributed across all terms when solving

Answer 1

Your friend made a mistake in their approach to solving the equation \( 7^{(x + 2)} = 7^{(3x - 8)} \). When the bases are the same, we can set the exponents equal to each other, rather than manipulating the bases as your friend did.

So, we start by setting the exponents equal to each other:

\[ x + 2 = 3x - 8 \]

Next, you can solve for \( x \):

1. Subtract \( x \) from both sides: \[ 2 = 2x - 8 \]

2. Add 8 to both sides: \[ 10 = 2x \]

3. Divide both sides by 2: \[ x = 5 \]

So the correct answer is \( x = 5 \).

Given this, the answer to the question about your friend's method is: "This is not correct. When the bases are the same, we can set the exponents equal to each other and solve that equation."