0.01=2.2^-t/8 solve for t?

Question

I cant figure out how to solve for t since it is in the exponential place. -t/8 is the power 2.2 is raised to.

Answer 1

Take the log of both sides:
log(0.01) = log(2.2^-t/8)

Remember that log(a^b) = b * log(a), so bring the -t/8 in front:
log(0.01) = -t/8 * log(2.2)

Now just solve algebraically:
-t/8 = log(0.01) / log(2.2)
t = -8 * log(0.01) / log(2.2)

log(0.01) = -2
log(2.2) ≈ 0.342422681

t = (-8 * -2) / 0.0.342422681
t = 16 / 0.342422681

Therefore:
t ≈ 46.7258768

As a double check, you can plug it in your calculator:
2.2^(-46.7258768/8) = 0.01

Answer 2

1) Take the natural log (ln) of both sides.
2) Move the (-t/8) in front of the ln(2.2)
3) Divide both sides by ln(2.2)
4) Solve for t.

Answer 3

0.01=2.2^-t/8 take ln of both sides
ln .01=-(t/8)ln 2.2
-t/8=ln .01 / ln 2.2
t=-8 ln .01 / ln 2.2=46.726