What is the answer to -19.7=20log_{10}(1/x) ?

The answer to -19.7=20log_{10}(1/x) is x=10^{0.985}

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-19.7=20log_{10}(1/x)

- 19.7 = 20 lo g_{10} (\frac{1}{x})

x = 1 0^{0.985}

Decimal Notation

x = 9.66050 \dots

Solution steps

- 19.7 = 20 lo g_{10} (\frac{1}{x})

Switch sides

20 lo g_{10} (\frac{1}{x}) = - 19.7

Divide both sides by

20

lo g_{10} (\frac{1}{x}) = - 0.985

Apply log rules

\frac{1}{x} = 1 0^{- 0.985}

Multiply both sides by

x

\frac{1}{x} x = 1 0^{- 0.985} x

Simplify

1 0^{- 0.985} x : \frac{1}{1 0 ^{0.985}} x

1 = \frac{1}{1 0 ^{0.985}} x

Solve

1 = \frac{1}{1 0 ^{0.985}} x : x = 1 0^{0.985}

x = 1 0^{0.985}

Verify Solutions:

x = 1 0^{0.985}

True

The solution is

x = 1 0^{0.985}

ln (1 + x) n = 5

ln (8) - ln (k + 2) = ln (k)

lo g_{2} (4 X) = 3

lo g_{9} (30 x^{2}) = 7

lo g_{x} (81) = 8

What is the answer to -19.7=20log_{10}(1/x) ?
The answer to -19.7=20log_{10}(1/x) is x=10^{0.985}
Solve for x: -19.7=20log_{10}(1/x)
The solution is x=10^{0.985}