Basic Math Examples

$2 = 2^{- 0.16 t}$

Step 1

Rewrite the equation as $2^{- 0.16 t} = 2$ .

$2^{- 0.16 t} = 2$

Step 2

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

$2^{- 0.16 t} = 2^{1}$

Step 3

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

$- 0.16 t = 1$

Step 4

Divide each term in $- 0.16 t = 1$ by $- 0.16$ and simplify.

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Step 4.1

Divide each term in $- 0.16 t = 1$ by $- 0.16$ .

$\frac{- 0.16 t}{- 0.16} = \frac{1}{- 0.16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 0.16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 0.16 t}{- 0.16} = \frac{1}{- 0.16}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{1}{- 0.16}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $1$ by $- 0.16$ .

$t = - 6.25$