Question

Use the laws of exponents to solve for x in the equation 7294x−1=93x+8
.(1 point)
Responses

x=196

x equals Start Fraction 19 over 6 End Fraction

x=119

x equals Start Fraction 11 over 6 End Fraction

x=9

x equals 9

x=−32

x equals negative Start Fraction 3 over 2 End Fraction

Answer 1

Interpret the equation as 729^(4x−1) = 9^(3x+8).

Write both sides with base 3: 729 = 3^6 and 9 = 3^2, so
(3^6)^(4x−1) = (3^2)^(3x+8)
=> 3^{6(4x−1)} = 3^{2(3x+8)}

Equate exponents:
6(4x−1) = 2(3x+8)
24x − 6 = 6x + 16
18x = 22
x = 22/18 = 11/9.

None of the listed multiple-choice answers equal 11/9.