Review – Exponential and Logarithmic Equations

Logarithms are used to find the number to which the base must be raised in order to become the value in the logarithm.

This is the method used when solving a logarithm problem:

If log_ax = N, then a^N = x.

I will work through two examples:

Example #1:
log₁₀10,000 = x
10^x = 10,000
x = 4

Example #2:
log₆12x = 2
6² = 12x
36 = 12x
x = 3


Natural logarithms, represented by ln, are logarithms with the base of e.

This is the method used when solving a natural logarithm problem:

If e^y = x, then ln(x) = y.

I will work through an example:

e^x = 30
ln(e^x) = ln(30)
x = ln(30)
x = ~3.4012