6.6 Homework: what are logarithms good for, anyway?

I invest $300 in a bank that pays 5% interest, compounded annually. So after $t$ years, I have $300(1.05{)}^t$ dollars in the bank. When I come back, I find that my account is worth $1000. How many years has it been? Your answer will not be a number—it will be a formula with a log in it.

The pH of a substance is given by the formula $\mathrm{pH}=-{\text{log}}_{10}\left[H^{+}\right]$ , if the concentration of Hydrogen ions.

• a If the Hydrogen concentration is $\frac{1}{10000}$ , what is the pH?
• b If the Hydrogen concentration is $\frac{1}{1000000}$ , what is the pH?
• c What happens to the pH every time the Hydrogen concentration divides by 10?

In the space below, write the question that $\text{log}\left(x\right)$ asks.

$\text{log}100$

$\text{log}1000$

$\text{log}10000$

$\text{log}\text{( 1 with n 0s after it )}$

$\text{log}500\text{(use the log button on your calculator)}$

$\text{ln}\left(e\right)=$

$\text{ln}\left(1\right)=$

$\text{ln}\left(0\right)=$

$\text{ln}\left({\mathrm{e}}^5\right)=$

$\text{ln}\left(3\right)=$ (*this is the only one that requires the ln button on your calculator)