What is the answer to ln(x+9)-ln(x+7)=3 ?

The answer to ln(x+9)-ln(x+7)=3 is x=(7e^3-9)/(1-e^3)

Solve for x: ln(x+9)-ln(x+7)=3

The solution is x=(7e^3-9)/(1-e^3)

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ln (x + 9) - ln (x + 7) = 3

x = \frac{7 e ^{3} - 9}{1 - e ^{3}}

Decimal Notation

x = - 6.89520 \dots

Solution steps

ln (x + 9) - ln (x + 7) = 3

Add

ln (x + 7)

to both sides

ln (x + 9) - ln (x + 7) + ln (x + 7) = 3 + ln (x + 7)

Simplify

ln (x + 9) = 3 + ln (x + 7)

Apply log rules

x + 9 = e^{3} (x + 7)

Solve

x + 9 = e^{3} (x + 7) : x = \frac{7 e ^{3} - 9}{1 - e ^{3}}

x = \frac{7 e ^{3} - 9}{1 - e ^{3}}

Verify Solutions:

x = \frac{7 e ^{3} - 9}{1 - e ^{3}}

True

The solution is

x = \frac{7 e ^{3} - 9}{1 - e ^{3}}

lo g_{10} (x + 1) = lo g_{10} (x) + 1

lo g_{3} (\frac{1}{x}) = - 2

lo g_{2} (x - 2) - 7 = - lo g_{2} (x + 6)

lo g_{10} (x - 21) = 2 - lo g_{10} (x)

lo g_{5} (x + 2) = 1 - lo g_{5} (x + 6)

What is the answer to ln(x+9)-ln(x+7)=3 ?
The answer to ln(x+9)-ln(x+7)=3 is x=(7e^3-9)/(1-e^3)
Solve for x: ln(x+9)-ln(x+7)=3
The solution is x=(7e^3-9)/(1-e^3)