Question

question
solve for x:
$27^{3x - 3} = 81^{2x + 4}$

Explanation:

Step1: Rewrite bases as powers of 3

$27 = 3^3$, $81 = 3^4$, so substitute:
$$(3^3)^{3x-3} = (3^4)^{2x+4}$$

Step2: Apply exponent power rule

Use $(a^m)^n = a^{m \cdot n}$ to simplify:
$$3^{3(3x-3)} = 3^{4(2x+4)}$$

Step3: Set exponents equal (same base)

Since bases are equal, exponents must be equal:
$$3(3x-3) = 4(2x+4)$$

Step4: Expand both sides of equation

Calculate the products:
$$9x - 9 = 8x + 16$$

Step5: Isolate x variable

Subtract $8x$ and add 9 to both sides:
$$9x - 8x = 16 + 9$$

Answer:

$x = 25$