Precalculus Examples

$\log (5 + r) = \log (5 s - 2)$

Step 1

Rewrite the equation as $\log (5 s - 2) = \log (5 + r)$ .

$\log (5 s - 2) = \log (5 + r)$

Step 2

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

$5 s - 2 = 5 + r$

Step 3

Solve for $s$ .

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Step 3.1

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

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Step 3.1.1

Add $2$ to both sides of the equation.

$5 s = 5 + r + 2$

Step 3.1.2

Add $5$ and $2$ .

$5 s = r + 7$

Step 3.2

Divide each term in $5 s = r + 7$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 s = r + 7$ by $5$ .

$\frac{5 s}{5} = \frac{r}{5} + \frac{7}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 s}{5} = \frac{r}{5} + \frac{7}{5}$

Step 3.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{r}{5} + \frac{7}{5}$