From an example question in my calc textbook:

Solve for $t$ in two steps, using a calculator at the final stage:

$$t\log 1.034 = \log P - \log 12.853$$

$$t = \frac{\log P}{\log 1.034} - \frac{\log 12.853}{\log 1.034}$$

$$t = 68.868 \log P - 76.375$$

Right, so I know that the $76.375$ comes from dividing $\dfrac{\log 12.853}{\log 1.034}$, but I can't for the life of me figure out what happened to get to $68.868 \log P$. Any help?


If the logarithms are common logarithms, i.e. to base $10$, you can see on a calculator that

$$\frac 1{\log 1.034}\approx 68.8679681017$$

Therefore we get

$$\frac {\log P}{\log 1.034}\approx 68.868\log P$$

Is the link between the equations now clear?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.