What is the answer to 2log_{10}(z)-log_{10}(z+7)=1 ?

The answer to 2log_{10}(z)-log_{10}(z+7)=1 is z=5+sqrt(95)

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2log_{10}(z)-log_{10}(z+7)=1

2 lo g_{10} (z) - lo g_{10} (z + 7) = 1

z = 5 + 95

Decimal Notation

z = 14.74679 \dots

Solution steps

2 lo g_{10} (z) - lo g_{10} (z + 7) = 1

Apply log rules

z^{2} = 10 (z + 7)

Solve

z^{2} = 10 (z + 7) : z = 5 + 95, z = 5 - 95

z = 5 + 95, z = 5 - 95

Verify Solutions:

z = 5 + 95

True

, z = 5 - 95

False

The solution is

z = 5 + 95

lo g_{x} (3) = \frac{1}{4}

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

0 = lo g_{3} (6 t + 27) - 5

11200 = 2100 \cdot lo g_{10} (x + 1)

lo g_{10} ((x + 1)^{2}) = 4

What is the answer to 2log_{10}(z)-log_{10}(z+7)=1 ?
The answer to 2log_{10}(z)-log_{10}(z+7)=1 is z=5+sqrt(95)
Solve for z: 2log_{10}(z)-log_{10}(z+7)=1
The solution is z=5+sqrt(95)