Calculus Examples Exponential and Logarithmic Functions

Solve for x

$4^{3 x + 2} = 4$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$4^{3 x + 2} = 4^{1}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$3 x + 2 = 1$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Subtract $2$ from both sides of the equation.

$3 x = 1 - 2$

Step 3.1.2

Subtract $2$ from $1$ .

$3 x = - 1$

Step 3.2

Divide each term in $3 x = - 1$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 x = - 1$ by $3$ .

$\frac{3 x}{3} = \frac{- 1}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 1}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{3}$

Decimal Form:

$x = - 0.\overline{3}$

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Exponential and Logarithmic Functions

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