Trigonometry Examples

$y = 7 {(1.2)}^{x}$

Step 1

Rewrite the equation as $7 \cdot {1.2}^{x} = y$ .

$7 \cdot {1.2}^{x} = y$

Step 2

Divide each term in $7 \cdot {1.2}^{x} = y$ by $7$ and simplify.

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Step 2.1

Divide each term in $7 \cdot {1.2}^{x} = y$ by $7$ .

$\frac{7 \cdot {1.2}^{x}}{7} = \frac{y}{7}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7 \cdot {1.2}^{x}}{7} = \frac{y}{7}$

Step 2.2.1.2

Divide ${1.2}^{x}$ by $1$ .

${1.2}^{x} = \frac{y}{7}$

Step 3

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

$\ln ({1.2}^{x}) = \ln (\frac{y}{7})$

Step 4

Expand $\ln ({1.2}^{x})$ by moving $x$ outside the logarithm.

$x \ln (1.2) = \ln (\frac{y}{7})$

Step 5

Divide each term in $x \ln (1.2) = \ln (\frac{y}{7})$ by $\ln (1.2)$ and simplify.

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Step 5.1

Divide each term in $x \ln (1.2) = \ln (\frac{y}{7})$ by $\ln (1.2)$ .

$\frac{x \ln (1.2)}{\ln (1.2)} = \frac{\ln (\frac{y}{7})}{\ln (1.2)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (1.2)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \ln (1.2)}{\ln (1.2)} = \frac{\ln (\frac{y}{7})}{\ln (1.2)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{y}{7})}{\ln (1.2)}$