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

Question

1437 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-15T04:53:44

#x = (17ln(0.8))/(ln2) ≈ -5.4727#

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#