What is the answer to log_{5}(x+7)+log_{5}(x-4)=3 ?

The answer to log_{5}(x+7)+log_{5}(x-4)=3 is x=(-3+3sqrt(69))/2

Solve for x: log_{5}(x+7)+log_{5}(x-4)=3

The solution is x=(-3+3sqrt(69))/2

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lo g_{5} (x + 7) + lo g_{5} (x - 4) = 3

x = \frac{- 3 + 3 69}{2}

Decimal Notation

x = 10.95993 \dots

Solution steps

lo g_{5} (x + 7) + lo g_{5} (x - 4) = 3

Apply log rules

(x + 7) (x - 4) = 125

Solve

(x + 7) (x - 4) = 125 : x = \frac{- 3 + 3 69}{2}, x = \frac{- 3 - 3 69}{2}

x = \frac{- 3 + 3 69}{2}, x = \frac{- 3 - 3 69}{2}

Verify Solutions:

x = \frac{- 3 + 3 69}{2}

True

, x = \frac{- 3 - 3 69}{2}

False

The solution is

x = \frac{- 3 + 3 69}{2}

∣ ln (x + 3) ∣ = 1

lo g_{3} (4) + lo g_{3} (x) = 1

7.4 = lo g_{10} (x)

y, ln (y) = e^{x} + ln (x)

lo g_{4} (8 x + 1) = 2

What is the answer to log_{5}(x+7)+log_{5}(x-4)=3 ?
The answer to log_{5}(x+7)+log_{5}(x-4)=3 is x=(-3+3sqrt(69))/2
Solve for x: log_{5}(x+7)+log_{5}(x-4)=3
The solution is x=(-3+3sqrt(69))/2