What is the answer to log_{3}(x+7)-log_{3}(x+1)=3 ?

The answer to log_{3}(x+7)-log_{3}(x+1)=3 is x=-10/13

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log_{3}(x+7)-log_{3}(x+1)=3

lo g_{3} (x + 7) - lo g_{3} (x + 1) = 3

x = - \frac{10}{13}

Decimal Notation

x = - 0.76923 \dots

Solution steps

lo g_{3} (x + 7) - lo g_{3} (x + 1) = 3

Add

lo g_{3} (x + 1)

to both sides

lo g_{3} (x + 7) - lo g_{3} (x + 1) + lo g_{3} (x + 1) = 3 + lo g_{3} (x + 1)

Simplify

lo g_{3} (x + 7) = 3 + lo g_{3} (x + 1)

Apply log rules

x + 7 = 27 (x + 1)

Solve

x + 7 = 27 (x + 1) : x = - \frac{10}{13}

x = - \frac{10}{13}

Verify Solutions:

x = - \frac{10}{13}

True

The solution is

x = - \frac{10}{13}

lo g_{10} (x) = - 1.45

93 = 10 lo g_{10} (x^{2})

7.8 = - lo g_{10} (x)

lo g_{3} (16 + 2 x) = 13

lo g_{10} (x) = - 1.22

What is the answer to log_{3}(x+7)-log_{3}(x+1)=3 ?
The answer to log_{3}(x+7)-log_{3}(x+1)=3 is x=-10/13
Solve for x: log_{3}(x+7)-log_{3}(x+1)=3
The solution is x=-10/13