What is the answer to ln(x+10)-ln(x+4)=3 ?

The answer to ln(x+10)-ln(x+4)=3 is x=(4e^3-10)/(1-e^3)

Solve for x: ln(x+10)-ln(x+4)=3

The solution is x=(4e^3-10)/(1-e^3)

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ln (x + 10) - ln (x + 4) = 3

x = \frac{4 e ^{3} - 10}{1 - e ^{3}}

Decimal Notation

x = - 3.68562 \dots

Solution steps

ln (x + 10) - ln (x + 4) = 3

Add

ln (x + 4)

to both sides

ln (x + 10) - ln (x + 4) + ln (x + 4) = 3 + ln (x + 4)

Simplify

ln (x + 10) = 3 + ln (x + 4)

Apply log rules

x + 10 = e^{3} (x + 4)

Solve

x + 10 = e^{3} (x + 4) : x = \frac{4 e ^{3} - 10}{1 - e ^{3}}

x = \frac{4 e ^{3} - 10}{1 - e ^{3}}

Verify Solutions:

x = \frac{4 e ^{3} - 10}{1 - e ^{3}}

True

The solution is

x = \frac{4 e ^{3} - 10}{1 - e ^{3}}

- ln (1 - 2 y) = 0

ln (z) - 1 = 1

lo g_{3} (4 x + 8) = lo g_{3} (x + 2)

2 lo g_{10} (x) = 8

lo g_{2} (x + 2) = lo g_{2} (7 x)

What is the answer to ln(x+10)-ln(x+4)=3 ?
The answer to ln(x+10)-ln(x+4)=3 is x=(4e^3-10)/(1-e^3)
Solve for x: ln(x+10)-ln(x+4)=3
The solution is x=(4e^3-10)/(1-e^3)