Question

solve for x.
\\( 3^{(-6x + 15)} = 81^x \\)
a. \\( x = \frac{2}{3} \\)
b. \\( x = \frac{3}{2} \\)
c. \\( x = -\frac{3}{2} \\)
d. \\( x = -\frac{2}{3} \\)

Explanation:

Step1: Rewrite base 81 as power of 3

$81 = 3^4$, so $81^x = (3^4)^x = 3^{4x}$

Step2: Set exponents equal (same base)

$-6x + 15 = 4x$

Step3: Isolate x terms

$15 = 4x + 6x$
$15 = 10x$

Step4: Solve for x

$x = \frac{15}{10} = \frac{3}{2}$

Answer:

B. $x = \frac{3}{2}$