*We're asked to solve the log of x plus log of 3 is equal to 2 log of 4 minus log of 2. So we have the log of x plus the log of 3 is equal to 2 times the log of 4 minus the log of 2, or the logarithm of 2. Whenever you see a logarithm written without a base, the implicit base is 10.*

The base unit is the number being raised to a power. When you see ln, it means natural logarithm (we'll define natural logarithms below).

In this course only base ten and natural logarithms will be used.

First we must get the log by itself by moving the 2 and the 5: The base of the log is 3, so we must raise both sides of the equation to be powers of 3: On the left hand side, the 3 and cancel, leaving just x - 1.

This lesson will discuss two ways to solve logarithmic equations.

The following graph shows one of the estimates for world population growth during the 21st century.

We see that the population will be 11 billion by about 2100!

Here's the graph of `y = ln (x 2)^2 - 2`, based on the first expression: So while the Log Law says we can write `ln (x 2)^2` as `2ln (x 2),` they are not really the same function.

The population of the earth is growing at approximately `1.3%` per year.

The following diagram shows how logarithm and exponents are related.

To get the second line, we actually raise `2` to the power of the left side, and `2` to the power of the right side.

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