Algebra Examples

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

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

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

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

Step 2

Use the quotient property of logarithms,

\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})

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

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

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

Step 3

Cancel the common factor of

x

$x$ .

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Step 3.1

Cancel the common factor.

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

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

Step 3.2

Divide

4

$4$ by

1

$1$ .

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

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

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

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

Step 4

Add

7

$7$ and

5

$5$ .

\log_{5} (4) = 12

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

Step 5

The equation is never true.

No solution