What is the answer to ln(x+1)-ln(x-2)=ln(x^2) ?

The answer to ln(x+1)-ln(x-2)=ln(x^2) is x\approx 2.54681…

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ln(x+1)-ln(x-2)=ln(x^2)

ln (x + 1) - ln (x - 2) = ln (x^{2})

x \approx 2.54681 \dots

Solution steps

ln (x + 1) - ln (x - 2) = ln (x^{2})

Add

ln (x - 2)

to both sides

ln (x + 1) - ln (x - 2) + ln (x - 2) = ln (x^{2}) + ln (x - 2)

Simplify

ln (x + 1) = ln (x^{2}) + ln (x - 2)

Apply log rules

x + 1 = x^{2} (x - 2)

Solve

x + 1 = x^{2} (x - 2) : x \approx 2.54681 \dots

x \approx 2.54681 \dots

Verify Solutions:

x \approx 2.54681 \dots

True

The solution is

x \approx 2.54681 \dots

lo g_{10} (x) = - 1.9852

lo g_{5} (x) = 3 - lo g_{5} (x - 20)

k = lo g_{2} (k) + 1

lo g_{\frac{1}{2}} (x) = 1024

ln (2 x + 5) = 0

What is the answer to ln(x+1)-ln(x-2)=ln(x^2) ?
The answer to ln(x+1)-ln(x-2)=ln(x^2) is x\approx 2.54681…
Solve for x: ln(x+1)-ln(x-2)=ln(x^2)
The solution is x\approx 2.54681…