Trigonometry Examples

$6 \cdot 17^{- 8 x} = 79$

Step 1

Divide each term in $6 \cdot 17^{- 8 x} = 79$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 \cdot 17^{- 8 x} = 79$ by $6$ .

$\frac{6 \cdot 17^{- 8 x}}{6} = \frac{79}{6}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 \cdot 17^{- 8 x}}{6} = \frac{79}{6}$

Step 1.2.1.2

Divide $17^{- 8 x}$ by $1$ .

$17^{- 8 x} = \frac{79}{6}$

Step 2

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

$\ln (17^{- 8 x}) = \ln (\frac{79}{6})$

Step 3

Expand $\ln (17^{- 8 x})$ by moving $- 8 x$ outside the logarithm.

$- 8 x \ln (17) = \ln (\frac{79}{6})$

Step 4

Divide each term in $- 8 x \ln (17) = \ln (\frac{79}{6})$ by $- 8 \ln (17)$ and simplify.

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Step 4.1

Divide each term in $- 8 x \ln (17) = \ln (\frac{79}{6})$ by $- 8 \ln (17)$ .

$\frac{- 8 x \ln (17)}{- 8 \ln (17)} = \frac{\ln (\frac{79}{6})}{- 8 \ln (17)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 8 x \ln (17)}{- 8 \ln (17)} = \frac{\ln (\frac{79}{6})}{- 8 \ln (17)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{x \ln (17)}{\ln (17)} = \frac{\ln (\frac{79}{6})}{- 8 \ln (17)}$

Step 4.2.2

Cancel the common factor of $\ln (17)$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{x \ln (17)}{\ln (17)} = \frac{\ln (\frac{79}{6})}{- 8 \ln (17)}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{79}{6})}{- 8 \ln (17)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = - \frac{\ln (\frac{79}{6})}{8 \ln (17)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\ln (\frac{79}{6})}{8 \ln (17)}$

Decimal Form:

$x = - 0.11372636 \dots$