Solve for x 5*2^x=5/16

$5 \cdot 2^{x} = \frac{5}{16}$

Divide each term in $(5 \cdot 2^{x}) = \frac{5}{16}$ by $5$ and simplify.

Divide each term in $(5 \cdot 2^{x}) = \frac{5}{16}$ by $5$ .

$\frac{(5 \cdot 2^{x})}{5} = \frac{\frac{5}{16}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 \cdot 2^{x}}{5} = \frac{\frac{5}{16}}{5}$

Divide $2^{x}$ by $1$ .

$2^{x} = \frac{\frac{5}{16}}{5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$2^{x} = \frac{5}{16} \cdot \frac{1}{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$2^{x} = \frac{5}{16} \cdot \frac{1}{5}$

Rewrite the expression.

$2^{x} = \frac{1}{16}$

Raise $16$ to the power of $1$ .

$2^{x} = \frac{1}{16^{1}}$

Move $16^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{x} = 16^{- 1}$

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

$2^{x} = 2^{- 4}$

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

$x = - 4$