close

Вход

Забыли?

вход по аккаунту

код для вставкиСкачать
Section 8.6
Solving Exponential and Logarithmic Equations
One way to solve exponential equations is to use the property that if two powers with the same
base are equal, then their exponents must be equal.
For b > 0 and b ≠ 1, if bx = by, then x = y.
Example #1
Solve 43x = 8x + 1.
SOLUTION
43x = 8x + 1
(22)3x = (23)x + 1
26x = 23x + 3
Write original equation.
Rewrite each power with base 2.
Power of a power property
6x = 3x + 3
x=1
Equate exponents.
Solve for x.
Sample Problem #1
Solve 24x = 32x – 1
When it is not convenient to write each side of an exponential equation using the same base, you
can solve the equation by taking a logarithm of each side.
Example #2
Solve 2x = 7
SOLUTION
2x = 7
log2 2x = log2 7
x = log2 7
x ≈ 2.807
****
Write original equation.
Take log2 of each side.
logb b x = x
Use a calculator
Sample Problem #2
Solve 4x = 15
Sample Problem #3
Solve 102x - 3 + 4 = 21
To solve a logarithmic equation, use this property for logarithms with the same base: For
positive numbers b, x, and y where b ≠ 1, logb x = logb y if and only if x = y.
Example #3
Solve log3 (5x - 1) = log3 (x + 7).
SOLUTION
log3 (5x - 1) = log3 (x + 7)
5x - 1 = x + 7
5x = x + 8
x=2
Write original equation.
Use property stated above.
Add 1 to each side.
Solve for x.
Sample Problem #4
Solve log4 (x + 3) = log4 (8x + 17).
Example #4
Solve log5 (3x + 1) = 2
log5 (3x + 1) = 2
52 = (3x + 1)
25 = 3x + 1
24 = 3x
8=x
Convert to an exponential equation
Sample Problem #5
Solve
log4 (x + 3) = 2
1/--страниц
Пожаловаться на содержимое документа