How do you solve $2^{\frac{x}{17}} = 0.8$ $2^(x/17) = 0.8$ ?

Question

1709 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-15T04:53:44

$x = \frac{17 ln (0.8)}{ln 2} \approx - 5.4727$ $x = (17ln(0.8))/(ln2) ≈ -5.4727$

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

$2^{\frac{x}{17}} = 0.8$ $2^(x/17) = 0.8$

$ln (2) \cdot \frac{x}{17} = ln (0.8)$ $ln(2) * (x)/(17) = ln(0.8)$

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

$ln (2) \cdot x = 17 ln (0.8)$ $ln(2) * x = 17ln(0.8)$

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

$x = \frac{17 ln (0.8)}{ln 2} \approx - 5.4727$ $x = (17ln(0.8))/(ln2) ≈ -5.4727$

How do you solve 2x17=0.82^(x/17) = 0.8?