Solve the equation by expressing each side as a power of the same base and then equating exponents. 6^{x - 6} = 1 / 1296

Solution:

Given, the equation is 6^{x - 6} = 1 / 1296

We have to express each side as a power of the same base and then equate the exponents.

Expressing 1296 with base 6 

6⁴ = 1296

Substituting in the given equation, we get

6^{x - 6} = 1/6⁴

6^{x - 6} = 6^-4

Since the bases are the same, then

x - 6 = -4

x = -4 + 6

x = 2

Therefore, the value of x in the given equation is 2.

Solve the equation by expressing each side as a power of the same base and then equating exponents. 6^{x - 6} = 1 / 1296

Summary:

Solving the equation 6^{x - 6} = 1 / 1296 by expressing each side as a power of the same base and then equating exponents, the value of x is 2.