What is 1/2 log_{2}(7)-2log_{2}(5) ?

The solution to 1/2 log_{2}(7)-2log_{2}(5) is log_{2}((sqrt(7))/(25))

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simplify 1/2 log_{2}(7)-2log_{2}(5)

simplify

\frac{1}{2} lo g_{2} (7) - 2 lo g_{2} (5)

lo g_{2} (\frac{7}{25})

Decimal Notation

- 3.24017 \dots

Solution steps

\frac{1}{2} lo g_{2} (7) - 2 lo g_{2} (5)

\frac{1}{2} lo g_{2} (7) = lo g_{2} (7^{\frac{1}{2}})

- 2 lo g_{2} (5) = - lo g_{2} (5^{2})

= lo g_{2} (7^{\frac{1}{2}}) - lo g_{2} (5^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (7^{\frac{1}{2}}) - lo g_{2} (5^{2}) = lo g_{2} (\frac{7 ^{\frac{1}{2}}}{5 ^{2}})

= lo g_{2} (\frac{7 ^{\frac{1}{2}}}{5 ^{2}})

5^{2} = 25

= lo g_{2} (\frac{7 ^{\frac{1}{2}}}{25})

Apply exponent rule:

a^{\frac{1}{2}} = a

7^{\frac{1}{2}} = 7

= lo g_{2} (\frac{7}{25})

lo g_{10} (\frac{9 x}{y})

ln (\frac{6 x 1 + 8 x}{( x - 4 ) ^{13}})

2 lo g_{10} (x) + 5 lo g_{10} (y)

lo g_{10} (x) + lo g_{10} (x - 3)

2 ln (2) - ln (3)

What is 1/2 log_{2}(7)-2log_{2}(5) ?
The solution to 1/2 log_{2}(7)-2log_{2}(5) is log_{2}((sqrt(7))/(25))