Trigonometry Examples

$6 \cdot 2^{4 x} = 21$

Step 1

Divide each term in $6 \cdot 2^{4 x} = 21$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 \cdot 2^{4 x} = 21$ by $6$ .

$\frac{6 \cdot 2^{4 x}}{6} = \frac{21}{6}$

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.

$\frac{6 \cdot 2^{4 x}}{6} = \frac{21}{6}$

Step 1.2.1.2

Divide $2^{4 x}$ by $1$ .

$2^{4 x} = \frac{21}{6}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $21$ and $6$ .

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Step 1.3.1.1

Factor $3$ out of $21$ .

$2^{4 x} = \frac{3 (7)}{6}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $3$ out of $6$ .

$2^{4 x} = \frac{3 \cdot 7}{3 \cdot 2}$

Step 1.3.1.2.2

Cancel the common factor.

$2^{4 x} = \frac{3 \cdot 7}{3 \cdot 2}$

Step 1.3.1.2.3

Rewrite the expression.

$2^{4 x} = \frac{7}{2}$

Step 2

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

$\ln (2^{4 x}) = \ln (\frac{7}{2})$

Step 3

Expand $\ln (2^{4 x})$ by moving $4 x$ outside the logarithm.

$4 x \ln (2) = \ln (\frac{7}{2})$

Step 4

Divide each term in $4 x \ln (2) = \ln (\frac{7}{2})$ by $4 \ln (2)$ and simplify.

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Step 4.1

Divide each term in $4 x \ln (2) = \ln (\frac{7}{2})$ by $4 \ln (2)$ .

$\frac{4 x \ln (2)}{4 \ln (2)} = \frac{\ln (\frac{7}{2})}{4 \ln (2)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x \ln (2)}{4 \ln (2)} = \frac{\ln (\frac{7}{2})}{4 \ln (2)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (\frac{7}{2})}{4 \ln (2)}$

Step 4.2.2

Cancel the common factor of $\ln (2)$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (\frac{7}{2})}{4 \ln (2)}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{7}{2})}{4 \ln (2)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{7}{2})}{4 \ln (2)}$

Decimal Form:

$x = 0.45183873 \dots$