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Logarithms Equation Example
- Question:
- Given: lg(x + 3)3 - lg2(x + 3) - 2 = 0, What is the value of x?
- Solution:
- lg(x + 3)3 - lg2(x + 3) - 2 = 0
- lg2(x + 3) - lg(x + 3)3 + 2 = 0
- lg2(x + 3) - 3 lg(x + 3) + 2 = 0
- let t = lg(x + 3), then lg2(x + 3) - 3 lg(x + 3) + 2 = 0 change to:
- t2 - 3t + 2 = 0
- (t - 2) (t - 1) = 0
- t1 = 2 and t2 = 1
- substitute the value of t to the equation t = lg(x + 3)
- equation1:
- 2 = lg(x + 3)
- 102 = x + 3
- x = 102 - 3
- x = 97
- equation2:
- 1 = lg(x + 3)
- 101 = x + 3
- x = 10 - 3
- x = 7
- The solution is: x1 = 7 and x2 = 97
- Formula used in this example:
- logabx = x logab
- If ax = b (a > 0 and a is not equal to 1), then x = logab
- when a = 10, log10b = lg b