Algebra Examples

$\log_{0.5} (x) = \log_{3} (2) + x$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\log_{3} (2)$ from both sides of the equation.

$\log_{0.5} (x) - \log_{3} (2) = x$

Step 1.2

Subtract $x$ from both sides of the equation.

$\log_{0.5} (x) - \log_{3} (2) - x = 0$

Step 2

Factor $- 1$ out of $\log_{0.5} (x) - \log_{3} (2) - x$ .

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Step 2.1

Reorder the expression.

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Step 2.1.1

Move $- \log_{3} (2)$ .

$\log_{0.5} (x) - x - \log_{3} (2) = 0$

Step 2.1.2

Reorder $\log_{0.5} (x)$ and $- x$ .

$- x + \log_{0.5} (x) - \log_{3} (2) = 0$

Step 2.2

Factor $- 1$ out of $- x$ .

$- (x) + \log_{0.5} (x) - \log_{3} (2) = 0$

Step 2.3

Factor $- 1$ out of $\log_{0.5} (x)$ .

$- (x) - 1 (- \log_{0.5} (x)) - \log_{3} (2) = 0$

Step 2.4

Factor $- 1$ out of $- \log_{3} (2)$ .

$- (x) - 1 (- \log_{0.5} (x)) - (\log_{3} (2)) = 0$

Step 2.5

Factor $- 1$ out of $- (x) - 1 (- \log_{0.5} (x))$ .

$- (x - \log_{0.5} (x)) - (\log_{3} (2)) = 0$

Step 2.6

Factor $- 1$ out of $- (x - \log_{0.5} (x)) - (\log_{3} (2))$ .

$- (x - \log_{0.5} (x) + \log_{3} (2)) = 0$