Algebra Examples

$0.6 = 5^{0.94 x + 4} - 2$

Step 1

Rewrite the equation as $5^{0.94 x + 4} - 2 = 0.6$ .

$5^{0.94 x + 4} - 2 = 0.6$

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

$5^{0.94 x + 4} = 0.6 + 2$

Step 2.2

Add $0.6$ and $2$ .

$5^{0.94 x + 4} = 2.6$

Step 3

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

$\ln (5^{0.94 x + 4}) = \ln (2.6)$

Step 4

Expand $\ln (5^{0.94 x + 4})$ by moving $0.94 x + 4$ outside the logarithm.

$(0.94 x + 4) \ln (5) = \ln (2.6)$

Step 5

Simplify the left side.

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Step 5.1

Simplify $(0.94 x + 4) \ln (5)$ .

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Step 5.1.1

Apply the distributive property.

$0.94 x \ln (5) + 4 \ln (5) = \ln (2.6)$

Step 5.1.2

Multiply $\ln (5)$ by $0.94$ .

$1.51287163 x + 4 \ln (5) = \ln (2.6)$

Step 6

Move all the terms containing a logarithm to the left side of the equation.

$4 \ln (5) - \ln (2.6) = - 1.51287163 x$

Step 7

Rewrite the equation as $- 1.51287163 x = 4 \ln (5) - \ln (2.6)$ .

$- 1.51287163 x = 4 \ln (5) - \ln (2.6)$

Step 8

Divide each term in $- 1.51287163 x = 4 \ln (5) - \ln (2.6)$ by $- 1.51287163$ and simplify.

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Step 8.1

Divide each term in $- 1.51287163 x = 4 \ln (5) - \ln (2.6)$ by $- 1.51287163$ .

$\frac{- 1.51287163 x}{- 1.51287163} = \frac{4 \ln (5)}{- 1.51287163} + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $- 1.51287163$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{- 1.51287163 x}{- 1.51287163} = \frac{4 \ln (5)}{- 1.51287163} + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x = \frac{4 \ln (5)}{- 1.51287163} + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3

Simplify the right side.

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Step 8.3.1

Simplify each term.

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Step 8.3.1.1

Move the negative in front of the fraction.

$x = - \frac{4 \ln (5)}{1.51287163} + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3.1.2

Factor $4$ out of $4 \ln (5)$ .

$x = - \frac{4 \ln (5)}{1.51287163} + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3.1.3

Factor $1.51287163$ out of $1.51287163$ .

$x = - \frac{4 \ln (5)}{1.51287163 (1)} + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3.1.4

Separate fractions.

$x = - (\frac{4}{1.51287163} \cdot \frac{\ln (5)}{1}) + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3.1.5

Divide $4$ by $1.51287163$ .

$x = - (2.64397844 \frac{\ln (5)}{1}) + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3.1.6

Divide $\ln (5)$ by $1$ .

$x = - (2.64397844 \ln (5)) + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3.1.7

Multiply $2.64397844$ by $- 1$ .

$x = - 2.64397844 \ln (5) + \frac{- \ln (2.6)}{- 1.51287163}$

Step 8.3.1.8

Dividing two negative values results in a positive value.

$x = - 2.64397844 \ln (5) + \frac{\ln (2.6)}{1.51287163}$

Step 8.3.1.9

Multiply by $1$ .

$x = - 2.64397844 \ln (5) + \frac{1 \ln (2.6)}{1.51287163}$

Step 8.3.1.10

Factor $1.51287163$ out of $1.51287163$ .

$x = - 2.64397844 \ln (5) + \frac{1 \ln (2.6)}{1.51287163 (1)}$

Step 8.3.1.11

Separate fractions.

$x = - 2.64397844 \ln (5) + \frac{1}{1.51287163} \cdot \frac{\ln (2.6)}{1}$

Step 8.3.1.12

Divide $1$ by $1.51287163$ .

$x = - 2.64397844 \ln (5) + 0.66099461 \frac{\ln (2.6)}{1}$

Step 8.3.1.13

Divide $\ln (2.6)$ by $1$ .

$x = - 2.64397844 \ln (5) + 0.66099461 \ln (2.6)$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = - 2.64397844 \ln (5) + 0.66099461 \ln (2.6)$

Decimal Form:

$x = - 3.62373123 \dots$