Algebra Examples

$\log_{2} (4 x - 3) = \log_{2} (3) + \log_{2} (x)$

Step 1

Simplify the right side.

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Step 1.1

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

$\log_{2} (4 x - 3) = \log_{2} (3 x)$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$4 x - 3 = 3 x$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $3 x$ from both sides of the equation.

$4 x - 3 - 3 x = 0$

Step 3.1.2

Subtract $3 x$ from $4 x$ .

$x - 3 = 0$

Step 3.2

Add $3$ to both sides of the equation.

$x = 3$