Precalculus Examples

$7 = 49^{3 x}$

Step 1

Rewrite the equation as $49^{3 x} = 7$ .

$49^{3 x} = 7$

Step 2

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

$7^{2 (3 x)} = 7^{1}$

Step 3

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

$2 (3 x) = 1$

Step 4

Solve for $x$ .

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Step 4.1

Multiply $3$ by $2$ .

$6 \cdot x = 1$

Step 4.2

Divide each term in $6 \cdot x = 1$ by $6$ and simplify.

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Step 4.2.1

Divide each term in $6 \cdot x = 1$ by $6$ .

$\frac{6 \cdot x}{6} = \frac{1}{6}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $6$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{6 \cdot x}{6} = \frac{1}{6}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{6}$

Decimal Form:

$x = 0.1\overline{6}$