Trigonometry Examples

$4 (3^{x}) = 20$

Step 1

Divide each term in $4 \cdot 3^{x} = 20$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 \cdot 3^{x} = 20$ by $4$ .

$\frac{4 \cdot 3^{x}}{4} = \frac{20}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 \cdot 3^{x}}{4} = \frac{20}{4}$

Step 1.2.1.2

Divide $3^{x}$ by $1$ .

$3^{x} = \frac{20}{4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $20$ by $4$ .

$3^{x} = 5$

Step 2

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

$\ln (3^{x}) = \ln (5)$

Step 3

Expand $\ln (3^{x})$ by moving $x$ outside the logarithm.

$x \ln (3) = \ln (5)$

Step 4

Divide each term in $x \ln (3) = \ln (5)$ by $\ln (3)$ and simplify.

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Step 4.1

Divide each term in $x \ln (3) = \ln (5)$ by $\ln (3)$ .

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (5)}{\ln (3)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $\ln (3)$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{\ln (5)}{\ln (3)}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (5)}{\ln (3)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (5)}{\ln (3)}$

Decimal Form:

$x = 1.46497352 \dots$