Algebra Examples

$\log_{5} (10 x - 1) = \log_{5} (9 x + 7)$

Step 1

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

$10 x - 1 = 9 x + 7$

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

Subtract $9 x$ from both sides of the equation.

$10 x - 1 - 9 x = 7$

Step 2.1.2

Subtract $9 x$ from $10 x$ .

$x - 1 = 7$

Step 2.2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.2.1

Add $1$ to both sides of the equation.

$x = 7 + 1$

Step 2.2.2

Add $7$ and $1$ .

$x = 8$