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. Solve for x in the equation log (7x+5) -log(x - 1) = 1(with full working​

User Ngenator
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1 Answer

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Answer:

Explanation:

To solve this equation, we can start by using the logarithm property that states: log(a) - log(b) = log(a/b).

Then, we can apply this property to the left side of the equation:

log (7x+5) - log(x - 1) = log((7x+5)/(x - 1)) = 1

Next, we can rewrite the right side of the equation as:

log((7x+5)/(x - 1)) = log(7x+5) - log(x - 1) = 1

Now, we can use the inverse property of logarithms, which states: log(a) = b, then a = 10^b, to solve for x.

This gives us: (7x+5)/(x - 1) = 10

We can then cross-multiply and simplify to get: 7x+5 = 10x - 10

This equation simplifies to: 3x = -5

Dividing both sides by 3 gives us: x = -5/3

Therefore, the solution to the equation is x = -5/3.

User Frenzy
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