Solve for x 2^(x-1)=1/64

$2^{x - 1} = \frac{1}{64}$

Step 1

Raise $64$ to the power of $1$ .

$2^{x - 1} = \frac{1}{64^{1}}$

Step 2

Move $64^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{x - 1} = 64^{- 1}$

Step 3

Create equivalent expressions in the equation that all have equal bases.

$2^{x - 1} = 2^{- 6}$

Step 4

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x - 1 = - 6$

Step 5

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$x = - 6 + 1$

Add $- 6$ and $1$ .

$x = - 5$