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Solve for c 1/27=3^c

$\frac{1}{27} = 3^{c}$

Step 1

Rewrite the equation as $3^{c} = \frac{1}{27}$ .

$3^{c} = \frac{1}{27}$

Step 2

Raise $27$ to the power of $1$ .

$3^{c} = \frac{1}{27^{1}}$

Step 3

Move $27^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{c} = 27^{- 1}$

Step 4

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

$3^{c} = 3^{- 3}$

Step 5

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

$c = - 3$

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