Solve for t. 9^t=4^t+1 Round the answer to three decimal places.

9^t = 4^(t + 1) ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ log both sides
t log 9 = (t + 1) log 4
t log 9 = t log 4 + log 4
t log 9 - t log 4 = log 4
t( log 9 - log 4) = log 4
t = log 4 / (log 9 - log 4)
t = 1.709511291 ≈ 1.710

If the right hand side is 4^(t+1) you can take the log of both sides.

t log 9 = (t + 1) log 4 = t log 4 + log 4

t log 9 - t log 4 = log 4
t (log 9 - log 4) = log 4

9^t = 4^(t+1)

take logs

t log(9) = (t+1)log(4)

0.9542t = 0.6020t + 0.6020

0.3522t = 0.6020

t = 0.602/0.3522

= 1.709

Looks like t=1/2

http://www.wolframalpha.com/input/?i=9%5Et%3D4%5Et%2B1