Algebra Examples

$- 6 \cdot 2^{0.1 x} = - 100$

Step 1

Simplify.

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Step 1.1

Divide each term in $- 6 \cdot 2^{0.1 x} = - 100$ by $- 6$ .

$\frac{- 6 \cdot 2^{0.1 x}}{- 6} = \frac{- 100}{- 6}$

Step 1.2

Cancel the common factor of $- 100$ and $- 6$ .

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Step 1.2.1

Factor $- 2$ out of $- 100$ .

$\frac{- 2 (50)}{- 6}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $- 2$ out of $- 6$ .

$\frac{- 2 \cdot 50}{- 2 \cdot 3}$

Step 1.2.2.2

Cancel the common factor.

$\frac{- 2 \cdot 50}{- 2 \cdot 3}$

Step 1.2.2.3

Rewrite the expression.

$\frac{50}{3}$

Step 1.3

Reduce by cancelling the common factors.

$2^{0.1 x} = \frac{50}{3}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(2)$ of the right side $(\frac{50}{3})$ equals the exponent $(0.1 x)$ .

$\log_{2} (\frac{50}{3}) = 0.1 x$