#1**0 **

Solve for t:

6^(3 t - 1) = 36^(t - 3)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):

log(6) (3 t - 1) = log(36) (t - 3)

Expand out terms of the left hand side:

3 log(6) t - log(6) = log(36) (t - 3)

Expand out terms of the right hand side:

3 log(6) t - log(6) = log(36) t - 3 log(36)

Subtract t log(36) - log(6) from both sides:

(3 log(6) - log(36)) t = log(6) - 3 log(36)

Divide both sides by 3 log(6) - log(36):

**t = (log(6) - 3 log(36))/(3 log(6) - log(36)) = - 5**

Guest Jul 7, 2020