помогите
Выразите
[tex] log_{ \sqrt{3} }( \sqrt[6]{1.5} ) [/tex]
через а если
[tex]a = log_{0.5}(27) [/tex]
Выразите
[tex] log_{ \sqrt{3} }( \sqrt[6]{1.5} ) [/tex]
через а если
[tex]a = log_{0.5}(27) [/tex]
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log(a^k) b^n = n/k log (a) b
log(a) b = 1/log(b) a
log(a) xy = log(a) |x| + log(a) |y|
log(√3) ⁶√1.5 = 1/6*2 log(3) 1.5 = 1/3 * log(3) 3*0.5 = 1/3 * log(3) 3 + 1/3*log(3) 0.5 = 1/3 + 1/3log(0.5) 3 = 1+ 1/log(0.5) 3^3 = 1/3 + 1/log(0.5) 27 = 1/3+1/a = (a + 3) / 3a
a = log(0.5) 27