To solve this equation, we first simplify the left side by using the properties of exponents.
3^4 - 5x * 3^(2x+6) = 1/18
3^4 = 81
5x 3^(2x+6) = 5x 3^2 3^6 = 5x 9 * 729 = 6561x
Now, the equation becomes:
81 - 6561x = 1/18
Rearranging the equation:
6561x = 81 - 1/18
6561x = (1458 - 1) / 18
6561x = 1457 / 18
x = 1457 / (18 * 6561)
x = 1457 / 118098
x ≈ 0.012347
Therefore, the value of x that satisfies the equation is approximately 0.012347.
To solve this equation, we first simplify the left side by using the properties of exponents.
3^4 - 5x * 3^(2x+6) = 1/18
3^4 = 81
5x 3^(2x+6) = 5x 3^2 3^6 = 5x 9 * 729 = 6561x
Now, the equation becomes:
81 - 6561x = 1/18
Rearranging the equation:
6561x = 81 - 1/18
6561x = (1458 - 1) / 18
6561x = 1457 / 18
x = 1457 / (18 * 6561)
x = 1457 / 118098
x ≈ 0.012347
Therefore, the value of x that satisfies the equation is approximately 0.012347.