Solve the exponential equation.

Question

18/1=27^2x−1

Answer 1

To solve the exponential equation, first rewrite it in a more simplified form:

18 = 27^(2x - 1)

Now, write both sides of the equation with the same base. Since 18 = 2 * 9, we can rewrite 18 as 2 * 9 = 2 * 3^2 = 6 * 3 = 3 * 2^2.

Therefore, the equation becomes:

3 * 2^2 = 3^(3(2x - 1))

Now, since both sides have the same base 3, we can compare the exponents:

2^2 = 3(2x - 1)

4 = 6x - 3

Add 3 to both sides:

7 = 6x

Divide both sides by 6:

x = 7/6

Therefore, the solution to the exponential equation is x = 7/6.