5-7

Mardi Gras Break Blog #1:
5-7
When solving for a variable as an exponent, you take the log of both sides. Then you bring the exponent to the front and solve.

EXAMPLE 1: Solve 10^x=4
A). Take the log of both the left and right side.
log 10^x = log 4
B). Now, bring the exponent to the front.
x log 10 = log 4
C). Solve for the variable, in this case x.
X = log 4/log 10

EXAMPLE 2: Solve 3^x=81
A). Take the log of both sides.
log 3^x = log 81
B). Bring the exponent to the front.
x log 3 = log 81
C). Solve for x.
x = log 81/log 3
D). Your final answer is 4.

To change a base given log b^a:
log x^a/ log x^b

EXAMPLE 1: Change log 3^7 to base 4.
A). Using the formula, you get
log 4^7/log 4^3