# How do you solve 2^(x/17) = 0.8?

Jul 15, 2016

x = (17ln(0.8))/(ln2) ≈ -5.4727

#### Explanation:

To solve for $x$, we first have to get rid of the exponent $\frac{x}{17}$. We can do this by taking the natural logarithm of both sides.

${2}^{\frac{x}{17}} = 0.8$

$\ln \left(2\right) \cdot \frac{x}{17} = \ln \left(0.8\right)$

Multiplying both sides by $17$ makes the left-hand side easier to solve for $x$, giving us

$\ln \left(2\right) \cdot x = 17 \ln \left(0.8\right)$

Dividing both sides by $\ln \left(2\right)$ isolates the $x$-term, so we now have

x = (17ln(0.8))/(ln2) ≈ -5.4727