What is the answer to 20log_{10}(x/2)=a ?

The answer to 20log_{10}(x/2)=a is x=5^{a/(20)}*2^{a/(20)+1}

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20log_{10}(x/2)=a

20 lo g_{10} (\frac{x}{2}) = a

x = 5^{\frac{a}{20}} \cdot 2^{\frac{a}{20} + 1}

Solution steps

20 lo g_{10} (\frac{x}{2}) = a

Divide both sides by

20

lo g_{10} (\frac{x}{2}) = \frac{a}{20}

Apply log rules

\frac{x}{2} = 1 0^{\frac{a}{20}}

Multiply both sides by

2

\frac{x}{2} \cdot 2 = 1 0^{\frac{a}{20}} \cdot 2

Simplify

1 0^{\frac{a}{20}} \cdot 2 : 5^{\frac{a}{20}} \cdot 2^{\frac{a}{20} + 1}

x = 5^{\frac{a}{20}} \cdot 2^{\frac{a}{20} + 1}

Verify Solutions:

x = 5^{\frac{a}{20}} \cdot 2^{\frac{a}{20} + 1}

True

The solution is

x = 5^{\frac{a}{20}} \cdot 2^{\frac{a}{20} + 1}

lo g_{10} (x) = \frac{3}{4}

ln (x) + ln (x - 1) = 2

lo g_{2} (5 x + 6) = 3

lo g_{10} (x + 13) = lo g_{10} (x) + lo g_{10} (13)

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

What is the answer to 20log_{10}(x/2)=a ?
The answer to 20log_{10}(x/2)=a is x=5^{a/(20)}*2^{a/(20)+1}