Algebra Examples

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

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

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)

$\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

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

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

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

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

$4 x - 3 = 3 x$

Step 3

Solve for

x

$x$ .

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Step 3.1

Move all terms containing

x

$x$ to the left side of the equation.

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Step 3.1.1

Subtract

3 x

$3 x$ from both sides of the equation.

4 x - 3 - 3 x = 0

$4 x - 3 - 3 x = 0$

Step 3.1.2

Subtract

3 x

$3 x$ from

4 x

$4 x$ .

x - 3 = 0

$x - 3 = 0$

x - 3 = 0

$x - 3 = 0$

Step 3.2

Add

3

$3$ to both sides of the equation.

x = 3

$x = 3$

x = 3

$x = 3$