What is the answer to |log_{10}(x)|=0.2 ?

The answer to |log_{10}(x)|=0.2 is x= 1/(10^{0.2)},x=10^{0.2}

Solve for x: |log_{10}(x)|=0.2

The solution is x= 1/(10^{0.2)},x=10^{0.2}

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∣ lo g_{10} (x) ∣ = 0.2

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

Decimal Notation

x = 0.63095 \dots, x = 1.58489 \dots

Solution steps

∣ lo g_{10} (x) ∣ = 0.2

Rewrite the equation with

lo g_{10} (x) = u

∣ u ∣ = 0.2

Solve

∣ u ∣ = 0.2 : u = - 0.2 or u = 0.2

u = - 0.2, u = 0.2

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = - 0.2 : x = \frac{1}{1 0 ^{0.2}}

Solve

lo g_{10} (x) = 0.2 : x = 1 0^{0.2}

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

Verify Solutions:

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

True

, x = 1 0^{0.2}

True

The solutions are

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

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

lo g_{9} (y) = 1

1.2 = lo g_{10} (x + 18)

4 - ln_{7} (p) = 0

lo g_{9} (y) = 7

What is the answer to |log_{10}(x)|=0.2 ?
The answer to |log_{10}(x)|=0.2 is x= 1/(10^{0.2)},x=10^{0.2}
Solve for x: |log_{10}(x)|=0.2
The solution is x= 1/(10^{0.2)},x=10^{0.2}