What is the answer to 2log_{10}(x)=(3+log_{10}(x))/(10) ?

The answer to 2log_{10}(x)=(3+log_{10}(x))/(10) is x=10^{3/19}

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2log_{10}(x)=(3+log_{10}(x))/(10)

2 lo g_{10} (x) = \frac{3 + lo g _{10} ( x )}{10}

x = 1 0^{\frac{3}{19}}

Decimal Notation

x = 1.43844 \dots

Solution steps

2 lo g_{10} (x) = \frac{3 + lo g _{10} ( x )}{10}

Multiply both sides by

10

2 lo g_{10} (x) \cdot 10 = \frac{3 + lo g _{10} ( x )}{10} \cdot 10

Simplify

20 lo g_{10} (x) = 3 + lo g_{10} (x)

Move

lo g_{10} (x)

to the left side

19 lo g_{10} (x) = 3

Divide both sides by

19

lo g_{10} (x) = \frac{3}{19}

Apply log rules

x = 1 0^{\frac{3}{19}}

Verify Solutions:

x = 1 0^{\frac{3}{19}}

True

The solution is

x = 1 0^{\frac{3}{19}}

lo g_{2} (x^{2}) = 1

lo g_{x} (8) + lo g_{x} (4) = 5

lo g_{10} ((x + 3)^{2}) - 2 = lo g_{10} (\frac{1}{( x ^{2} )})

a, lo g_{2} (a) - 3 lo g_{2} (b) = 2

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

What is the answer to 2log_{10}(x)=(3+log_{10}(x))/(10) ?
The answer to 2log_{10}(x)=(3+log_{10}(x))/(10) is x=10^{3/19}
Solve for x: 2log_{10}(x)=(3+log_{10}(x))/(10)
The solution is x=10^{3/19}