Question

What is the solution for log(t-3)=log(17-4t)

Answer 1

`\text{The domain}\\\\t-3 > 0\ \wedge\ 17-4t > 0\\\\t > 3\ \wedge\ t < (17)/(4)\to3<t<4(1)/(4)\\--------------------------------\\\\\log(t-3)=\log(17-4t)\iff t-3=17-4t\qquad\text{add 3 to both sides}\\\\t=20-4t\qquad\text{add 4t to both sides}\\\\5t=20\qquad\text{divide both sides by 5}\\\\\boxed{t=4}\in Domain`

Answer 2

log(t-3)=log(17-4t)

since they are both logs to the same base, what is inside must be the same

t-3 = 17 -4t

add 4t to each side

t-3+4t = 17-4t+4t

5t-3 = 17

add 3 to each side

5t -3+3 = 17+3

5t = 20

divide each side by 5

t =4