What is the answer to 2log_{10}(2x)=1+log_{10}(a) ?

The answer to 2log_{10}(2x)=1+log_{10}(a) is No Solution for x\in\mathbb{R}

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2log_{10}(2x)=1+log_{10}(a)

2 lo g_{10} (2 x) = 1 + lo g_{10} (a)

No Solution for x \in R

Solution steps

2 lo g_{10} (2 x) = 1 + lo g_{10} (a)

Divide both sides by

2

lo g_{10} (2 x) = \frac{1 + lo g _{10} ( a )}{2}

Apply log rules

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

Solve

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

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

Verify Solutions:

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

False

The solution is

No Solution for x \in R

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What is the answer to 2log_{10}(2x)=1+log_{10}(a) ?
The answer to 2log_{10}(2x)=1+log_{10}(a) is No Solution for x\in\mathbb{R}