When solving the problem 7^x+2 = 7^3x-8 , your friend does the following:
7(x)+2=7(3x)-8
7x+2=21x-8
10=14x
x=5/7
Was this correct?
A. The 7 needs to be distributed across all terms when solving.
B. When the bases are the same, then we can set the exponents equal to each other and solve that equation.
C.Yes, this is correct. No error was made. D. Both sides should be divided by 7 instead of multiplied by 7.
The correct answer is A. The 7 needs to be distributed across all terms when solving.
In the equation 7^(x+2) = 7^(3x-8), we cannot directly distribute the 7 to the terms inside the parentheses because the exponents are different. To distribute the 7, we need to rewrite the equation as (7^x)*(7^2) = (7^3)*(7^(-8)). Then we can combine like terms and set the exponents equal to each other.