Algebra Examples

$\log_{3} (x) + 5 = \log_{3} (2 x) + 10$

Step 1

Move all the terms containing a logarithm to the left side of the equation.

$\log_{3} (x) - \log_{3} (2 x) = - 5 + 10$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{3} (\frac{x}{2 x}) = - 5 + 10$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\log_{3} (\frac{x}{2 x}) = - 5 + 10$

Step 3.2

Rewrite the expression.

$\log_{3} (\frac{1}{2}) = - 5 + 10$

Step 4

Add $- 5$ and $10$ .

$\log_{3} (\frac{1}{2}) = 5$

Step 5

The equation is never true.

No solution