Question

1296^{x - 3} = 7776^4

Explanation:

Step1: Express bases as powers of 6

$1296 = 6^4$, $7776 = 6^5$
Substitute into equation:
$$(6^4)^{x-3} = (6^5)^4$$

Step2: Simplify exponents

Use exponent rule $(a^m)^n=a^{m \cdot n}$:
$$6^{4(x-3)} = 6^{20}$$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$$4(x-3) = 20$$

Step4: Solve for x

Divide both sides by 4:
$$x-3 = 5$$
Add 3 to both sides:
$$x = 5 + 3$$

Answer:

$x=8$