Algebra Examples

$\log_{7} (6) + 3 \log_{7} (2) = x$

Step 1

Rewrite the equation as $x = \log_{7} (6) + 3 \log_{7} (2)$ .

$x = \log_{7} (6) + 3 \log_{7} (2)$

Step 2

Simplify $\log_{7} (6) + 3 \log_{7} (2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify $3 \log_{7} (2)$ by moving $3$ inside the logarithm.

$x = \log_{7} (6) + \log_{7} (2^{3})$

Step 2.1.2

Raise $2$ to the power of $3$ .

$x = \log_{7} (6) + \log_{7} (8)$

Step 2.2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$x = \log_{7} (6 \cdot 8)$

Step 2.3

Multiply $6$ by $8$ .

$x = \log_{7} (48)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \log_{7} (48)$

Decimal Form:

$x = 1.98940378 \dots$