1)
log₂√₃1 = x
(2√3)ˣ = 1
(2√3)ˣ = (2√3)⁰
x = 0
Ответ: log₂√₃1 = 0
2)
[tex]log _{ \sqrt[4]{8} } 16 \sqrt[7]{4} =x[/tex]
[tex]( \sqrt[4]{8} )^{x}=16 \sqrt[7]{4} [/tex]
[tex] ( 2^{ \frac{3}{4} } )^{x} = 2^{4} * 2^{ \frac{2}{7} } [/tex]
[tex] 2^{ \frac{3x}{4} } = 2^{ \frac{30}{7} } [/tex]
[tex] \frac{3x}{4} = \frac{30}{7} [/tex]
[tex]3x*7=4*30[/tex]
[tex]x= \frac{4*30}{3*7}= \frac{40}{7}=5 \frac{5}{7} [/tex]
Ответ: [tex]log _{ \sqrt[4]{8} } 16 \sqrt[7]{4} = 5 \frac{5}{7} [/tex]
