Answer:
Step-by-step explanation:
log(x) + log(x-1) = log(4x)
The numbers that are separated by a plus sign (or a minus sign) can be combined as multiplication.
log5 + log10 = log50. You can try this yourself. log(5) + log(10) - log(50) = 0
So log(x) + log(x-1) = log(4x)
log(x)(x - 1) = log(4x) When you take the antilog of both sides, you get
(x)(x - 1) = 4x Remove the brackets
x^2 - x = 4x Subtract 4x from both sides.
x^2 - x - 4x = 4x - 4x Combine like terms.
x^2 - 5x = 0 Use the distributive law to take out the common factor
x(x - 5) = 0
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This means there are two answers
x = 0
x - 5 = 0
x = 5
x = 0 gives an error, so it is not a solution.
x = 5 gives 1 solution
Check
log(5) + log(5 -1) = log(4*5)
log(5) + log(4) = log(20)
0.6989 + 0.6021 = 1.3010
1.03010 = 1.3010
x^2 - 5x = 0
