What is the point of logarithms? How are they used? Why do you need logarithms?
In what situations do you use them?

Logarithms are primarily used for two thing:
i) Representation of large numbers. For example pH(the number of hydrogen atoms present) is too large (up to 10 digits). To allow easier representation of these numbers, logarithms are used.
For example let's say the pH of the substance is $10000000000$. 
This can written as $10^{10}$. 
Or let the pH of another substance be $1000000$. This can be written as $10^6$. Note the base is always the same, but the exponent is unique. Therefore the log of the substance can be used to identify the substance. For example the first substance can be represented as $log$ $10000000000$ or $10$ and the second substance can be represented as $log$ $1000000$ or $6$. Note $6$ and $10$ are much easier to deal with.
But what if you're not a chemist? How would you use logs?
ii) Algebra.
Let's say you have the equation $316 = 10^x$. How would you solve for $x$? You could find the log of $316$ which is approximately $2.5$. The equation would then be $10^{2.5} = 10^x$. Therefore $x$ is $2.5$. Logs are therefore extremely useful when solving for exponents.
Note that although I have restricted my examples to log base 10 for simplicity, logs can exist in other bases. For example $\log_2 32$ (log to the base 2 of 32) is $5$ since $2^5= 32$. Other important log bases include the the natural log, which is commonly used in advanced mathematics. 
What other appliances do logs have? Logs have a variety of real life applications such as calculating half lives and exponential growth/decay. In fact the inverse of an exponential function is a logarithmic function!
