What is simplify-0.9log_{2}(0.9)-0.1*log_{2}(0.05) ?

The solution to simplify-0.9log_{2}(0.9)-0.1*log_{2}(0.05) is -log_{2}(0.67408…)

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simplify-0.9log_{2}(0.9)-0.1*log_{2}(0.05)

simplify

- 0.9 lo g_{2} (0.9) - 0.1 \cdot lo g_{2} (0.05)

- lo g_{2} (0.67408 \dots)

Decimal Notation

0.56899 \dots

Solution steps

- 0.9 lo g_{2} (0.9) - 0.1 lo g_{2} (0.05)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.9 lo g_{2} (0.9) = lo g_{2} (0. 9^{0.9})

= - lo g_{2} (0. 9^{0.9}) - 0.1 lo g_{2} (0.05)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.1 lo g_{2} (0.05) = lo g_{2} (0.0 5^{0.1})

= - lo g_{2} (0. 9^{0.9}) - lo g_{2} (0.0 5^{0.1})

Rewrite

- lo g_{2} (0. 9^{0.9}) - lo g_{2} (0.0 5^{0.1})

- (lo g_{2} (0. 9^{0.9}) + lo g_{2} (0.0 5^{0.1}))

= - (lo g_{2} (0. 9^{0.9}) + lo g_{2} (0.0 5^{0.1}))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (0. 9^{0.9}) + lo g_{2} (0.0 5^{0.1}) = lo g_{2} (0. 9^{0.9} \cdot 0.0 5^{0.1})

= - lo g_{2} (0. 9^{0.9} \cdot 0.0 5^{0.1})

0. 9^{0.9} \cdot 0.0 5^{0.1} = 0.67408 \dots

= - lo g_{2} (0.67408 \dots)

ln (\frac{6561}{64}) - \frac{9}{4} + 3 ln (3) - 12 ln (2) + 3

- ln (2 x - 2) + ln (2 x - 4)

4 ln (2) - 5 ln (3)

10 \cdot lo g_{10} (1 0^{\frac{a}{10}} - 1 0^{\frac{b}{10}})

lo g_{10} (\frac{m}{7})

What is simplify-0.9log_{2}(0.9)-0.1*log_{2}(0.05) ?
The solution to simplify-0.9log_{2}(0.9)-0.1*log_{2}(0.05) is -log_{2}(0.67408…)