How do you solve 6^ { 2x + 3} \cdot 6^ { 1- x } = \frac { 1} { 6}?

1 Answer
May 4, 2017

x=-3

Explanation:

convert 1/6 to a power of 6:

1/a^m = a^-m

1/6^1 = 6^-1

this gives you:

6^(2x+3) * 6^(1-x) = 6^-1

law of indices:
a^m * a^n = a^(m+n)

using this:

6^(2x+3) * 6^(1-x) = 6^(2x+3+1-x) = 6^-1

this gives the equation
2x+3+1-x = -1

collect like terms:
x+4 = -1

subtract 4:

x=-3