Use substitution to evaluate a definite integral with rational or logarithmic functions

Question

Determine the value of the following definite integral ∫6log₉(t) [7,8] Enter an exact answer, for example,{3(ln6+ln4−1)}/ln7. Please explain each step in detail. Thank you!

Answer 1

t=9^a

log₉(t)=a

ln t = a ln 9 =log₉(t) ln 9

log₉(t)=(ln t)/ln 9

Now the only other thing you need to know is ∫ln t dt which is t ln t - t