Algebra Examples

$2 = 6 {(2)}^{0.99 x} - 9$

Step 1

Rewrite the equation as $6 \cdot 2^{0.99 x} - 9 = 2$ .

$6 \cdot 2^{0.99 x} - 9 = 2$

Step 2

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

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Step 2.1

Add $9$ to both sides of the equation.

$6 \cdot 2^{0.99 x} = 2 + 9$

Step 2.2

Add $2$ and $9$ .

$6 \cdot 2^{0.99 x} = 11$

Step 3

Divide each term in $6 \cdot 2^{0.99 x} = 11$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 \cdot 2^{0.99 x} = 11$ by $6$ .

$\frac{6 \cdot 2^{0.99 x}}{6} = \frac{11}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 \cdot 2^{0.99 x}}{6} = \frac{11}{6}$

Step 3.2.1.2

Divide $2^{0.99 x}$ by $1$ .

$2^{0.99 x} = \frac{11}{6}$

Step 4

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (2^{0.99 x}) = \ln (\frac{11}{6})$

Step 5

Expand the left side.

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Step 5.1

Expand $\ln (2^{0.99 x})$ by moving $0.99 x$ outside the logarithm.

$0.99 x \ln (2) = \ln (\frac{11}{6})$

Step 5.2

Multiply $\ln (2)$ by $0.99$ .

$0.6862157 x = \ln (\frac{11}{6})$

Step 6

Divide each term in $0.6862157 x = \ln (\frac{11}{6})$ by $0.6862157$ and simplify.

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Step 6.1

Divide each term in $0.6862157 x = \ln (\frac{11}{6})$ by $0.6862157$ .

$\frac{0.6862157 x}{0.6862157} = \frac{\ln (\frac{11}{6})}{0.6862157}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $0.6862157$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{0.6862157 x}{0.6862157} = \frac{\ln (\frac{11}{6})}{0.6862157}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{11}{6})}{0.6862157}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Replace $e$ with an approximation.

$x = \frac{\log_{2.71828182} (\frac{11}{6})}{0.6862157}$

Step 6.3.2

Divide $11$ by $6$ .

$x = \frac{\log_{2.71828182} (1.8\overline{3})}{0.6862157}$

Step 6.3.3

Log base $2.71828182$ of $1.8\overline{3}$ is approximately $0.6061358$ .

$x = \frac{0.6061358}{0.6862157}$

Step 6.3.4

Divide $0.6061358$ by $0.6862157$ .

$x = 0.88330213$