What is the answer to log_{4}(x)+log_{10}(8x)=1 ?

The answer to log_{4}(x)+log_{10}(8x)=1 is x=10^{(2log_{10}(2)-6log_{10}(2)^2)/(1+2log_{10)(2)}}

Solve for x: log_{4}(x)+log_{10}(8x)=1

The solution is x=10^{(2log_{10}(2)-6log_{10}(2)^2)/(1+2log_{10)(2)}}

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lo g_{4} (x) + lo g_{10} (8 x) = 1

x = 1 0^{\frac{2 l o g _{10} ( 2 ) - 6 l o g _{10} ( 2 ) ^{2}}{1 + 2 l o g _{10} ( 2 )}}

Decimal Notation

x = 1.08747 \dots

Solution steps

lo g_{4} (x) + lo g_{10} (8 x) = 1

Apply log rules

x = 1 0^{\frac{2 l o g _{10} ( 2 ) - 6 l o g _{10} ( 2 ) ^{2}}{1 + 2 l o g _{10} ( 2 )}}

Verify Solutions:

x = 1 0^{\frac{2 l o g _{10} ( 2 ) - 6 l o g _{10} ( 2 ) ^{2}}{1 + 2 l o g _{10} ( 2 )}}

True

The solution is

x = 1 0^{\frac{2 l o g _{10} ( 2 ) - 6 l o g _{10} ( 2 ) ^{2}}{1 + 2 l o g _{10} ( 2 )}}

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

lo g_{10} (x + 2) - lo g_{10} (x - 1) = 4

x^{1 + l o g_{10} (x)} = 10 x

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

2 lo g_{10} (x) - lo g_{10} (x + 6) = 0

What is the answer to log_{4}(x)+log_{10}(8x)=1 ?
The answer to log_{4}(x)+log_{10}(8x)=1 is x=10^{(2log_{10}(2)-6log_{10}(2)^2)/(1+2log_{10)(2)}}
Solve for x: log_{4}(x)+log_{10}(8x)=1
The solution is x=10^{(2log_{10}(2)-6log_{10}(2)^2)/(1+2log_{10)(2)}}