What is the answer to log_{7}(x+2)=2log_{7}(x-2) ?

The answer to log_{7}(x+2)=2log_{7}(x-2) is x=(5+sqrt(17))/2

Solve for x: log_{7}(x+2)=2log_{7}(x-2)

The solution is x=(5+sqrt(17))/2

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

x = \frac{5 + 17}{2}

Decimal Notation

x = 4.56155 \dots

Solution steps

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

Apply log rules

x + 2 = (x - 2)^{2}

Solve

x + 2 = (x - 2)^{2} : x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

x = \frac{5 + 17}{2}, x = \frac{5 - 17}{2}

Verify Solutions:

x = \frac{5 + 17}{2}

True

, x = \frac{5 - 17}{2}

False

The solution is

x = \frac{5 + 17}{2}

lo g_{x + 2} (3 x^{2} + 4 x - 14) = 2

ln (x^{2}) = 11

lo g_{2} (5 - x) - lo g_{2} (3 - x) = 2

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

lo g_{8} (x) = 1.5

What is the answer to log_{7}(x+2)=2log_{7}(x-2) ?
The answer to log_{7}(x+2)=2log_{7}(x-2) is x=(5+sqrt(17))/2
Solve for x: log_{7}(x+2)=2log_{7}(x-2)
The solution is x=(5+sqrt(17))/2