Question

Logarithms question! Help needed with part (iii). Please refer to attached image.

Answer 1

\[S=75-6\ln{(t+1)}\]\[S=62 = 75 - 6\ln{(t+1)}\]\[13=6\ln{(t+1})\]\[\frac{13}{6}=\ln{(t+1)}\]Raise e to both sides to eliminate ln\[e^{\frac{13}{6}}=t+1\]\[t = e^{\frac{13}{6}}-1 \approx 7.73\]

Should be able to express t in terms of S by following steps above.

\[S=75-6\ln{(t+1)}\]
\[S-75=-6\ln{(t+1)}\]
\[-\frac{(S-75)}{6} = \ln{(t+1)}\]
\[e^{-\frac{(S-75)}{6}} = t+1\]
Solve for t :-)

Answer 2

nicely explained @whpalmer4

Answer 3

ANY DOUBT@Bellyeflower

Answer 4

How to continue from e^(−(S−75)/6)=t+1, I don't know how...

Answer 5

How about subtracting 1 from each side, leaving you with an expression for t in terms of S? :-) e is the base of the natural logarithm (= 2.71828...), not something you need to find.

Answer 6

I misread the question, oops! But thank you anyway :)