What is the answer to ln(x+4)-ln(x)=3 ?

The answer to ln(x+4)-ln(x)=3 is x= 4/(e^3-1)

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ln(x+4)-ln(x)=3

ln (x + 4) - ln (x) = 3

x = \frac{4}{e ^{3} - 1}

Solution steps

ln (x + 4) - ln (x) = 3

Add

ln (x)

to both sides

ln (x + 4) - ln (x) + ln (x) = 3 + ln (x)

Simplify

ln (x + 4) = 3 + ln (x)

Apply log rules

x + 4 = e^{3} x

Solve

x + 4 = e^{3} x : x = \frac{4}{e ^{3} - 1}

x = \frac{4}{e ^{3} - 1}

Verify Solutions:

x = \frac{4}{e ^{3} - 1}

True

The solution is

x = \frac{4}{e ^{3} - 1}

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4 ln (x - 5) = - 4

What is the answer to ln(x+4)-ln(x)=3 ?
The answer to ln(x+4)-ln(x)=3 is x= 4/(e^3-1)
Solve for x: ln(x+4)-ln(x)=3
The solution is x= 4/(e^3-1)