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