What is 2log_{10}(sqrt(5))-1/2 log_{10}(5) ?

The solution to 2log_{10}(sqrt(5))-1/2 log_{10}(5) is 1/2 log_{10}(5)

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simplify 2log_{10}(sqrt(5))-1/2 log_{10}(5)

simplify

2 lo g_{10} (5) - \frac{1}{2} lo g_{10} (5)

\frac{1}{2} lo g_{10} (5)

Decimal Notation

0.34948 \dots

Solution steps

2 lo g_{10} (5) - \frac{1}{2} lo g_{10} (5)

Convert element to fraction:

2 lo g_{10} (5) = \frac{2 lo g _{10} ( 5 )}{1}

= \frac{2 lo g _{10} ( 5 )}{1} - \frac{1}{2} lo g_{10} (5)

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

= \frac{- \frac{1}{2} lo g _{10} ( 5 ) \cdot 1 + 2 lo g _{10} ( 5 )}{1}

Apply rule:

a \cdot 1 = a

- \frac{1}{2} lo g_{10} (5) \cdot 1 = - \frac{1}{2} lo g_{10} (5)

= \frac{- \frac{1}{2} lo g _{10} ( 5 ) + 2 lo g _{10} ( 5 )}{1}

Cancel

\frac{- \frac{1}{2} lo g _{10} ( 5 ) + 2 lo g _{10} ( 5 )}{1} : \frac{1}{2} lo g_{10} (5)

= \frac{1}{2} lo g_{10} (5)

2 ln (5 x^{2}) - ln (2 x^{2})

ln (\frac{5 x}{y})

- lo g_{10} (1.8 \cdot 1 0^{- 2})

lo g_{b} (9) + lo g_{b} (7)

ln (\frac{1 - x}{x})

What is 2log_{10}(sqrt(5))-1/2 log_{10}(5) ?
The solution to 2log_{10}(sqrt(5))-1/2 log_{10}(5) is 1/2 log_{10}(5)