What is the value of x in the equation ln (x + 6) - ln (2x - 1) = 1?
-0.21,0.74, 1.35, 1.97

Solution:

Given that:

ln (x + 6) - ln (2x - 1) = 1

Using logarithm rule:

ln a - ln b = ln (a/b)

ln((x + 6) / (2x - 1)) = 1

((x + 6) / (2x - 1)) = e¹

We know that,

e¹ = 2.72

((x + 6) / (2x - 1)) ≈ 2.72

Simplifying we get,

 (x + 6) = 2.72 (2x - 1)

x + 6 = 2.72 (2x) - 2.72 (1)

x + 6 = 5.44x - 2.72

8.72 = 4.44x

By cross multiplication we get,

x = 8.72 / 4.44

x = 1.97

Therefore, the value of x is 1.97.

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What is the value of x in the equation ln (x + 6) - ln (2x - 1) = 1?

Summary:

The value of x in the equation ln (x + 6) - ln (2x - 1) = 1 is 1.97.