Question

SOLVE 6^3^-X=6^2 FOR X A.X=-6B.X=1C.X=-1D.X=9​

Answer 1

Answer: Choice B) x = 1

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Explanation:

The problem should read 6^(3-x) = 6^2. The 3-x must be in parenthesis to indicate that all of "3-x" is in the exponent and not just the 3.

Because both bases are 6, and because both sides are equal, this means that the exponents must be equal as well. Therefore 3-x = 2. Let's solve for x

3-x = 2

3-x+x = 2+x .... adding x to both sides

3 = 2+x

2+x = 3 ..... flipping both sides

x+2 = 3

x+2-2 = 3-2 .... subtracting 2 from both sides

x = 1

You can use logarithms to solve this problem, but the fact that the bases are both the same allows us to use this faster shortcut.