Properties of Exponents: To review some of the fundamental properties of exponents, we will look at several examples.
If a > 0, b > 0, and x and y are any real numbers, then:

a^{x} ● a^{y} = a^{x+y}




Properties of Logarithms: To review some of the fundamental properties of logarithms, we will look at several examples.
If x and y are both positive numbers, then:
 Meaning of Log: If .
If
Notice: the log is the exponent.

log(x) + log(x + 2) = log(x^{2} + 2x)
Notice: if the base b is not shown, the base is assumed to be 10.



ln(x) means log_{e}(x) where .

Putting It All Together:
Solve for
x if
.
By direction inspection we can see that x must equal 4.
Solve for
x if
.
In this case, direct inspection fails us since 4 is too big  giving us 16  and 3 is too small  only giving us 8.
To get an exact answer, we would use logarithms:
Step 1:
Step 2:
Step 3:
Let's Practice. In the following five equations, solve for x (accurate to 3 decimal places).