Question

Solve the exponential equation by the method of relating the bases, first rewriting the equation in the form b^u = b^v: (81)^x = (1/3)^(x-4)

A) x = -3
B) x = -4
C) x = 4
D) x = 3

Answer 1

To solve the exponential equation (81)^x = (1/3)^(x-4), rewrite it in the form b^u = b^v and set the exponents equal to each other. The solution is x = 1.

Step-by-step explanation:

To solve the exponential equation (81)^x = (1/3)^(x-4), we can rewrite it in the form b^u = b^v. We know that 81 is equal to 3^4, so we rewrite the equation as (3^4)^x = (1/3)^(x-4).

Using the property that (a^b)^c = a^(b*c), we simplify the equation to 3^(4x) = (3^(-1))^(-x+4).

Now we have the bases equal, so we can set the exponents equal to each other: 4x = -x+4.

By combining like terms and solving for x, we get x = 1.