What is the answer to 2.8=-log_{10}((0.2)/x) ?

The answer to 2.8=-log_{10}((0.2)/x) is x=0.2*10^{2.8}

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2.8=-log_{10}((0.2)/x)

2.8 = - lo g_{10} (\frac{0.2}{x})

x = 0.2 \cdot 1 0^{2.8}

Decimal

x = 126.19146 \dots

Solution steps

2.8 = - lo g_{10} (\frac{0.2}{x})

Move

lo g_{10} (\frac{0.2}{x})

to the left side

2.8 + lo g_{10} (\frac{0.2}{x}) = 0

Move

2.8

to the right side

lo g_{10} (\frac{0.2}{x}) = - 2.8

Apply log rules

\frac{0.2}{x} = 1 0^{- 2.8}

Multiply both sides by

x

\frac{0.2}{x} x = 1 0^{- 2.8} x

Simplify

1 0^{- 2.8} x : \frac{1}{1 0 ^{2.8}} x

0.2 = \frac{1}{1 0 ^{2.8}} x

Solve

0.2 = \frac{1}{1 0 ^{2.8}} x : x = 0.2 \cdot 1 0^{2.8}

x = 0.2 \cdot 1 0^{2.8}

Verify Solutions:

x = 0.2 \cdot 1 0^{2.8}

True

The solution is

x = 0.2 \cdot 1 0^{2.8}

lo g_{10} (x) + lo g_{10} (x + 2) = 8

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

x, t (x) = lo g_{4} (x + 2)

ln (x) = \frac{3}{2}

ln (x^{2}) = 0

What is the answer to 2.8=-log_{10}((0.2)/x) ?
The answer to 2.8=-log_{10}((0.2)/x) is x=0.2*10^{2.8}
Solve for x: 2.8=-log_{10}((0.2)/x)
The solution is x=0.2*10^{2.8}