Question
Download Solution PDFlog (x + 3) + log (x + 5) = log 35, solve for x :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
log (x + 3) + log (x + 5) = log 35
Formula Used:
log a + log b = log (a × b)
If log a = log b, then a = b
Calculation:
Using the logarithm property log a + log b = log (a × b):
log [(x + 3)(x + 5)] = log 35
Since the logarithms on both sides are equal, their arguments must be equal:
(x + 3)(x + 5) = 35
x2 + 5x + 3x + 15 = 35
x2 + 8x + 15 - 35 = 0
x2 + 8x - 20 = 0
(x + 10)(x - 2) = 0
x + 10 = 0 ⇒ x = -10
x - 2 = 0 ⇒ x = 2
Logarithm of a negative number is undefined
So, x = 2 is a valid solution.
∴ The solution for x is 2.
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