Trigonometry Examples

3^{x + 4} = 4

$3^{x + 4} = 4$

Step 1

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

\ln (3^{x + 4}) = \ln (4)

$\ln (3^{x + 4}) = \ln (4)$

Step 2

Expand

\ln (3^{x + 4})

$\ln (3^{x + 4})$ by moving

x + 4

$x + 4$ outside the logarithm.

(x + 4) \ln (3) = \ln (4)

$(x + 4) \ln (3) = \ln (4)$

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

Apply the distributive property.

x \ln (3) + 4 \ln (3) = \ln (4)

$x \ln (3) + 4 \ln (3) = \ln (4)$

x \ln (3) + 4 \ln (3) = \ln (4)

$x \ln (3) + 4 \ln (3) = \ln (4)$

Step 4

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

x \ln (3) + 4 \ln (3) - \ln (4) = 0

$x \ln (3) + 4 \ln (3) - \ln (4) = 0$

Step 5

Move all terms not containing

x

$x$ to the right side of the equation.

Tap for more steps...

Step 5.1

Subtract

4 \ln (3)

$4 \ln (3)$ from both sides of the equation.

x \ln (3) - \ln (4) = - 4 \ln (3)

$x \ln (3) - \ln (4) = - 4 \ln (3)$

Step 5.2

Add

\ln (4)

$\ln (4)$ to both sides of the equation.

x \ln (3) = - 4 \ln (3) + \ln (4)

$x \ln (3) = - 4 \ln (3) + \ln (4)$

x \ln (3) = - 4 \ln (3) + \ln (4)

$x \ln (3) = - 4 \ln (3) + \ln (4)$

Step 6

Divide each term in

x \ln (3) = - 4 \ln (3) + \ln (4)

$x \ln (3) = - 4 \ln (3) + \ln (4)$ by

\ln (3)

$\ln (3)$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in

x \ln (3) = - 4 \ln (3) + \ln (4)

$x \ln (3) = - 4 \ln (3) + \ln (4)$ by

\ln (3)

$\ln (3)$ .

\frac{x \ln (3)}{\ln (3)} = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}

$\frac{x \ln (3)}{\ln (3)} = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of

\ln (3)

$\ln (3)$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

\frac{x \ln (3)}{\ln (3)} = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}

$\frac{x \ln (3)}{\ln (3)} = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}$

Step 6.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}

$x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}$

x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}

$x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}$

x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}

$x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Cancel the common factor of

\ln (3)

$\ln (3)$ .

Tap for more steps...

Step 6.3.1.1

Cancel the common factor.

x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}

$x = \frac{- 4 \ln (3)}{\ln (3)} + \frac{\ln (4)}{\ln (3)}$

Step 6.3.1.2

Divide

- 4

$- 4$ by

1

$1$ .

x = - 4 + \frac{\ln (4)}{\ln (3)}