Final answer:
To solve the equation 64^(2x+4) = 16^(5x), we express both sides as powers of 2, equate the exponents, and simplify to find that x = 3.
Step-by-step explanation:
To solve the equation 642x+4 = 165x, we can use the property of exponents that states when the bases are the same, the exponents must be equal for the equation to hold true.
Both 64 and 16 are powers of 2 (64 is 26 and 16 is 24). Using this relationship, we rewrite the equation by expressing 64 and 16 as powers of 2:
26(2x+4) = 24(5x)
Now that the bases are the same, we can equate the exponents:
6(2x+4) = 4(5x)
Simplify and solve for x:
- 12x + 24 = 20x
- 20x - 12x = 24
- 8x = 24
- x = 3
Therefore, the solution to the equation is x = 3.