Lesson 3.4, page 410 Exponential & Logarithmic Equations. Objective: To solve exponential and logarithmic equations. Why it’s important…. This skill can be used to solve many types of real-world problems, including those involving animal population. Solving with Same Base.
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Lesson 3.4, page 410Exponential & Logarithmic Equations
Objective: To solve exponential and logarithmic equations.
Example: 73x = 20
Property of Logarithmic Equality
For any M > 0, N > 0, a > 0, and a 1,
loga M = loga N
M = N
Solve: 2x = 50
This is an exact answer. We cannot simplify further, but we can approximate using a calculator.
We can check by finding 25.6439 50.
C) 3x+4 = 101 D) e0.25w = 12
log2 x = 16 and log x + log (x + 4) = 1,
are called logarithmic equations.
a) log2 (x – 4) = 3 b) 4 ln(3x) = 8
Solve: log x + log (x – 3) = 1.
Solve: log4x = 3
Check: For x = 3:
For x = 3:
Negative numbers do not have real-number logarithms. The solution is 3.
If log b M = log b N, then M = N.
Solve ln (x - 3) = ln (7x – 23) – ln (x + 1).
a) 75x = 3000b) 52x = 16
c) log(7 – 2x) = -1
d) log 6 – log 3x = -2