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Mathematics
Cali Benjamin
5 June, 18:56
What is the solution of log2x + 6 144 = 2?
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Kyle Bond
5 June, 20:19
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2x+6 is the base
Then the equation is logarithm of 144 on basis 2x + 6 = 2
Then [2x + 6]^2 = 144
Now expand the square binomial
4x^2 + 24x + 36 = 144
4x^2 + 24x + 36 - 144 = 0
4x^2 + 24x - 108 = 0
Divide by 4
x^2 + 6x - 27 = 0
Factor: (x + 9) (x - 3) = 0
x = - 9 and x = 3
The only valid is x = 3, because x = - 9 yields 2x + 6 = - 12 and the logarithm function cannot have negative basis.
Then the answer is x = 3.
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