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

1 Answer
Jul 15, 2016

x = (17ln(0.8))/(ln2) ≈ -5.4727

Explanation:

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

2^(x/17) = 0.8

ln(2) * (x)/(17) = ln(0.8)

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

ln(2) * x = 17ln(0.8)

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

x = (17ln(0.8))/(ln2) ≈ -5.4727