Solving $\ln y = 3t + 8$ for $y$

Question

Question:

Solve for $y$. $$\ln y = 3t + 8$$

I tried answering the question with $$(\ln x - 8)/3$$ but I am told it's wrong. I'm really confused with the logarithms unit, so any help would be very appreciated!

Answer 1

There is one single trick with logarithms: isolate a logarithm and exponentiate. In your case $\log y = 3t+8$ the logarithm is already isolated, so we exponentiate: $$ e^{\log y} = e^{3t+8} $$ but $e^{\log y} = y$, so $y = e^{3t+8}$.