What is 1/2 log_{2}(6)-2log_{2}(5) ?

The solution to 1/2 log_{2}(6)-2log_{2}(5) is log_{2}((sqrt(6))/(25))

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simplify 1/2 log_{2}(6)-2log_{2}(5)

simplify

\frac{1}{2} lo g_{2} (6) - 2 lo g_{2} (5)

lo g_{2} (\frac{6}{25})

Decimal Notation

- 3.35137 \dots

Solution steps

\frac{1}{2} lo g_{2} (6) - 2 lo g_{2} (5)

\frac{1}{2} lo g_{2} (6) = lo g_{2} (6^{\frac{1}{2}})

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

= lo g_{2} (6^{\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} (6^{\frac{1}{2}}) - lo g_{2} (5^{2}) = lo g_{2} (\frac{6 ^{\frac{1}{2}}}{5 ^{2}})

= lo g_{2} (\frac{6 ^{\frac{1}{2}}}{5 ^{2}})

5^{2} = 25

= lo g_{2} (\frac{6 ^{\frac{1}{2}}}{25})

Apply exponent rule:

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

6^{\frac{1}{2}} = 6

= lo g_{2} (\frac{6}{25})

\frac{1}{2} lo g_{2} (6) - 2 lo g_{2} (7)

3 ln (x^{3} y) + 2 ln (y z^{2})

ln (5) + ln (x)

lo g_{4} (x^{2} - 9) - 6 lo g_{4} (x + 3)

- lo g_{b} (\frac{1}{7})

What is 1/2 log_{2}(6)-2log_{2}(5) ?
The solution to 1/2 log_{2}(6)-2log_{2}(5) is log_{2}((sqrt(6))/(25))