What is the answer to 2log_{10}(x)-log_{10}(5)=-2 ?

The answer to 2log_{10}(x)-log_{10}(5)=-2 is x=10^{(-2+log_{10}(5))/2}

Solve for x: 2log_{10}(x)-log_{10}(5)=-2

The solution is x=10^{(-2+log_{10}(5))/2}

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2 lo g_{10} (x) - lo g_{10} (5) = - 2

x = 1 0^{\frac{- 2 + l o g _{10} ( 5 )}{2}}

Decimal Notation

x = 0.22360 \dots

Solution steps

2 lo g_{10} (x) - lo g_{10} (5) = - 2

Move

lo g_{10} (5)

to the right side

2 lo g_{10} (x) = - 2 + lo g_{10} (5)

Divide both sides by

2

lo g_{10} (x) = \frac{- 2 + lo g _{10} ( 5 )}{2}

Apply log rules

x = 1 0^{\frac{- 2 + l o g _{10} ( 5 )}{2}}

Verify Solutions:

x = 1 0^{\frac{- 2 + l o g _{10} ( 5 )}{2}}

True

The solution is

x = 1 0^{\frac{- 2 + l o g _{10} ( 5 )}{2}}

lo g_{2 - 3 k} (125) = 3

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

4 ln (x + 6) = - 8

lo g_{3} (x + a) = b

lo g_{3} (4 x - 5) - lo g_{3} (x + 2) = 1

What is the answer to 2log_{10}(x)-log_{10}(5)=-2 ?
The answer to 2log_{10}(x)-log_{10}(5)=-2 is x=10^{(-2+log_{10}(5))/2}
Solve for x: 2log_{10}(x)-log_{10}(5)=-2
The solution is x=10^{(-2+log_{10}(5))/2}