Answer:
B) 3
Step-by-step explanation:
To solve the exponential equation ( 7^{3 – 2x} = 7^{–x} ), you can follow these steps:
Step 1: Set the Exponents Equal to Each Other
Since the bases on both sides of the equation are the same (both are base 7), you can set the exponents equal to each other. That is because if ( a^b = a^c ), then ( b = c ) provided that ( a ) is not equal to 0.
Step 2: Solve for ( x )
Set the exponents equal to each other and solve for ( x ):
( 3 – 2x = –x )
Now, isolate ( x ) on one side:
( 3 = –x + 2x )
Combine like terms:
( 3 = x )
Step 3: Identify the Correct Answer
The solution to the equation is ( x = 3 ), which matches option B) 3.
Correct Answer: B) 3
Hope this helps!