What is simplify-0.093*log_{2}(0.093)-0.07*log_{2}(0.07) ?

The solution to simplify-0.093*log_{2}(0.093)-0.07*log_{2}(0.07) is -log_{2}(0.66561…)

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simplify-0.093log_{2}(0.093)-0.07log_{2}(0.07)

simplify

- 0.093 \cdot lo g_{2} (0.093) - 0.07 \cdot lo g_{2} (0.07)

- lo g_{2} (0.66561 \dots)

Decimal Notation

0.58723 \dots

Solution steps

- 0.093 lo g_{2} (0.093) - 0.07 lo g_{2} (0.07)

Apply log rule:

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

0.093 lo g_{2} (0.093) = lo g_{2} (0.09 3^{0.093})

= - lo g_{2} (0.09 3^{0.093}) - 0.07 lo g_{2} (0.07)

Apply log rule:

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

0.07 lo g_{2} (0.07) = lo g_{2} (0.0 7^{0.07})

= - lo g_{2} (0.09 3^{0.093}) - lo g_{2} (0.0 7^{0.07})

Rewrite

- lo g_{2} (0.09 3^{0.093}) - lo g_{2} (0.0 7^{0.07})

- (lo g_{2} (0.09 3^{0.093}) + lo g_{2} (0.0 7^{0.07}))

= - (lo g_{2} (0.0 7^{0.07}) + lo g_{2} (0.09 3^{0.093}))

Apply log rule:

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

lo g_{2} (0.09 3^{0.093}) + lo g_{2} (0.0 7^{0.07}) = lo g_{2} (0.09 3^{0.093} \cdot 0.0 7^{0.07})

= - lo g_{2} (0.09 3^{0.093} \cdot 0.0 7^{0.07})

0.09 3^{0.093} \cdot 0.0 7^{0.07} = 0.66561 \dots

= - lo g_{2} (0.66561 \dots)

ln (\frac{x + \frac{1}{2}}{x + 1})

ln (B e^{- a t})

e ln (ey) - e

- ln ∣ x + 2 ∣ + ln ∣ x ∣ + C

20 ln (\frac{21}{7})

What is simplify-0.093*log_{2}(0.093)-0.07*log_{2}(0.07) ?
The solution to simplify-0.093*log_{2}(0.093)-0.07*log_{2}(0.07) is -log_{2}(0.66561…)