Question

Помогите,пожалуйста, вычислить. Подробно.

Answer 1

$dfrac{log_714- frac{1}{3}log_756 }{log_630-0.5log_6150} = dfrac{log_714-log_7 sqrt[3]{56} }{log_630-log_6 sqrt{150} } = dfrac{log_7 frac{14}{ sqrt[3]{56} } }{log_6 frac{30}{ sqrt{150} } } =\ \ \ = dfrac{log_7 frac{14}{2 sqrt[3]{7} } }{log_6 frac{30}{5 sqrt{6} } } = dfrac{log_7(7^{1- frac{1}{3} })}{log_6(6^{1- frac{1}{2} })} = dfrac{1- frac{1}{3} }{1- frac{1}{2} } = dfrac{6-2}{6-3} = dfrac{4}{3}$

$dfrac{3log_72-0.5log_764}{4log_52+ frac{1}{3}log_527 } = dfrac{log_72^3-log_764^{ frac{1}{2} }}{log_52^4+log_5 sqrt[3]{27} } = dfrac{log_78-log_78}{log_516+log_53} =0$

Answer 2

2) 
(Loq₇ 14  -(1/3)*Log₇ 56 ) / (Log₆ 30 -(1/2)* Log₆ 150 ) =
( Loq₇ 2+Loq₇ 7  -(1/3)*(Log₇ 7 + Log₇ 2³ ) ) /
(Log₆ 6+Log₆ 5 -(1/2)*( Log₆ 6 + Log₆ 5² ) ) = 
( Loq₇ 2+1  -1/3  - Log₇ 2 ) / (1+ Log₆ 5 -1/2  - Log₆ 5 ) = (2/3) /(1/2) = 4/3 .
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4)
 (3Log₇ 2 -(1/2)*Log₇ 64) / (4Log₅ 2 +(1/3)*Log₅ 27) =
 (3Log₇ 2 -(1/2)*Log₇ 2⁶) / (4Log₅ 2 +(1/3)*Log₅ 3³)  =
 (3Log₇ 2 -(1/2)*6Log₇ 2 ) / (4Log₅ 2 +(1/3)*3Log₅ 3)  =0 /5Log₅ 2  =0.