When solving the problem 7^x+2 =7^3x-8 your friend does the following:

Question

7 (x) +2=7(3x)- 8

7x +2=21x-8
10=14x
X=5/7

Was this correct

Answer choices

A.) this is not correct. The 7 needs to be distributed across all terms when solving
B.) this is not correct. Both sides should be divided by 7 instead of multiplied by seven
C.) this is not correct. When the bases are the same, then we can set the exponents equal to each other and solve that equation
D.) this is correct there are no errors

Answer 1

In analyzing your friend's solution to the equation \( 7^{x+2} = 7^{3x-8} \), we can see that the friend made some mistakes in their steps.

The correct way to approach the problem is to recognize that since the bases are the same (both are base 7), we can set the exponents equal to each other. This is because if \( a^m = a^n \), then \( m = n \) when \( a \) is not zero or one.

So we can write:

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

From there, we can solve for \( x \):

1. Rearranging the equation gives: \[ x - 3x = -8 - 2 \] \[ -2x = -10 \] \[ x = 5 \]

Given this analysis, your friend's approach is flawed in that they incorrectly interpreted the equation. Hence, the correct option regarding your friend's solution is:

C.) this is not correct. When the bases are the same, then we can set the exponents equal to each other and solve that equation.