Basic Math Examples

$- 2 \cdot \log (5) \cdot (7 n) = 2$

Step 1

Multiply $7$ by $- 2$ .

$- 14 \log (5) \cdot n = 2$

Step 2

Divide each term in $(- 14 \log (5) \cdot n) = 2$ by $- 14 \log (5)$ and simplify.

Tap for more steps...

Divide each term in $(- 14 \log (5) \cdot n) = 2$ by $- 14 \log (5)$ .

$\frac{(- 14 \log (5) \cdot n)}{- 14 \log (5)} = \frac{2}{- 14 \log (5)}$

Simplify the left side.

Tap for more steps...

Cancel the common factor of $- 14$ .

Tap for more steps...

Cancel the common factor.

$\frac{- 14 \log (5) \cdot n}{- 14 \log (5)} = \frac{2}{- 14 \log (5)}$

Rewrite the expression.

$\frac{\log (5) \cdot n}{\log (5)} = \frac{2}{- 14 \log (5)}$

Cancel the common factor of $\log (5)$ .

Tap for more steps...

Cancel the common factor.

$\frac{\log (5) \cdot n}{\log (5)} = \frac{2}{- 14 \log (5)}$

Divide $n$ by $1$ .

$n = \frac{2}{- 14 \log (5)}$

Simplify the right side.

Tap for more steps...

Cancel the common factor of $2$ and $- 14$ .

Tap for more steps...

Factor $2$ out of $2$ .

$n = \frac{2 (1)}{- 14 \log (5)}$

Cancel the common factors.

Tap for more steps...

Factor $2$ out of $- 14 \log (5)$ .

$n = \frac{2 (1)}{2 (- 7 \log (5))}$

Cancel the common factor.

$n = \frac{2 \cdot 1}{2 (- 7 \log (5))}$

Rewrite the expression.

$n = \frac{1}{- 7 \log (5)}$

Simplify $- 7 \log (5)$ by moving $7$ inside the logarithm.

$n = \frac{1}{- \log (5^{7})}$

Raise $5$ to the power of $7$ .

$n = \frac{1}{- \log (78125)}$

Cancel the common factor of $1$ and $- 1$ .

Tap for more steps...

Rewrite $1$ as $- 1 (- 1)$ .

$n = \frac{- 1 (- 1)}{- \log (78125)}$

Move the negative in front of the fraction.

$n = - \frac{1}{\log (78125)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{1}{\log (78125)}$

Decimal Form:

$n = - 0.20438236 \dots$