Algebra Examples

$\log_{2} (3) (2 x - 1) = \log_{2} (3 x - 2)$

Step 1

Simplify $\log_{2} (3) (2 x - 1)$ .

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Step 1.1

Apply the distributive property.

$\log_{2} (3) (2 x) + \log_{2} (3) \cdot - 1 = \log_{2} (3 x - 2)$

Step 1.2

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

$\log_{2} (3^{2}) x + \log_{2} (3) \cdot - 1 = \log_{2} (3 x - 2)$

Step 1.3

Move $- 1$ to the left of $\log_{2} (3)$ .

$\log_{2} (3^{2}) x - 1 \cdot \log_{2} (3) = \log_{2} (3 x - 2)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$\log_{2} (9) x - 1 \cdot \log_{2} (3) = \log_{2} (3 x - 2)$

Step 1.4.2

Rewrite $- 1 \log_{2} (3)$ as $- \log_{2} (3)$ .

$\log_{2} (9) x - \log_{2} (3) = \log_{2} (3 x - 2)$

Step 1.5

Reorder factors in $\log_{2} (9) x - \log_{2} (3)$ .

$x \log_{2} (9) - \log_{2} (3) = \log_{2} (3 x - 2)$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution