# How do you solve 5(1+10^6x) = 12?

Oct 18, 2015

Rearrange and take logs if necessary to find $x$.

#### Explanation:

I'm not sure whether your question appears as intended, so I will answer both interpretations:

$\boldsymbol{5 \left(1 + {10}^{6} x\right) = 12}$

Divide both sides by $5$ to get:

$1 + {10}^{6} x = \frac{12}{5}$

Subtract $1$ from both sides to get:

${10}^{6} x = \frac{7}{5}$

Divide both sides by ${10}^{6}$ to get:

$x = \frac{7}{5 \cdot {10}^{6}} = 0.0000014$

$\boldsymbol{5 \left(1 + {10}^{6 x}\right) = 12}$

Divide both sides by $5$ to get:

$1 + {10}^{6 x} = \frac{12}{5}$

Subtract $1$ from both sides to get:

${10}^{6 x} = \frac{7}{5}$

Take common logarithms of both sides to get:

$6 x = \log \left(\frac{7}{5}\right)$

Divide both sides by $6$ to get:

$x = \log \frac{\frac{7}{5}}{6} \approx 0.02435$