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Express y in terms of x if Log 10 x + Log 10 ( Y )= 2 Log 10 (x+1) ​

User Ignat
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Using the properties of logarithms, we can simplify the left-hand side of the equation as follows:

Log 10 (x) + Log 10 (y) = Log 10 [(x)(y)]

Then, we can rewrite the right-hand side of the equation using the power rule of logarithms:

2 Log 10 (x+1) = Log 10 [(x+1)^2]

Substituting these expressions back into the original equation, we get:

Log 10 [(x)(y)] = Log 10 [(x+1)^2]

Using the fact that Log 10 (a) = Log 10 (b) if and only if a = b, we can drop the logarithm on both sides of the equation:

(x)(y) = (x+1)^2

Expanding the right-hand side, we obtain:

(x)(y) = x^2 + 2x + 1

Solving for y, we get:

y = (x^2 + 2x + 1)/x

Therefore, y can be expressed in terms of x as:

y = x + 2 + 1/x
User Snives
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