Algebra Examples

$\log_{5} (4 x) - 7 = \log_{5} (x) + 5$

Step 1

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

$\log_{5} (4 x) - \log_{5} (x) = 7 + 5$

Step 2

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

$\log_{5} (\frac{4 x}{x}) = 7 + 5$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\log_{5} (\frac{4 x}{x}) = 7 + 5$

Step 3.2

Divide $4$ by $1$ .

$\log_{5} (4) = 7 + 5$

Step 4

Add $7$ and $5$ .

$\log_{5} (4) = 12$

Step 5

The equation is never true.

No solution