Use the laws of exponents to solve for x in the equation 729^4x−1=93^x+8 .(1 point) Responses x=119 x equals Start Fraction 11 over 6 End Fraction x=−32 x equals negative Start Fraction 3 over 2 End Fraction x=9 x equals 9 x=196
To solve the equation, we can rewrite the numbers using the prime factorization:
729 = 3^6
93 = 3^1 * 31
So the equation becomes:
(3^6)^(4x-1) = (3^1 * 31)^(x+8)
Using the power of a power rule, we can simplify the left side of the equation:
3^(6 * (4x-1)) = (3^1 * 31)^(x+8)
3^(24x-6) = (3^(x+8)) * (31^(x+8))
Since both sides of the equation have a base of 3 raised to different exponents, we can set the exponents equal to each other:
24x-6 = x+8
Solving this equation will give us the value of x.
Subtracting x from both sides:
24x - x - 6 = x + 8 - x
23x - 6 = 8
Adding 6 to both sides:
23x = 14
Dividing by 23:
x = 14/23
Hence, x = 14/23.