Question

Помогите решить пожалуйста,заранее спасибо

Answer 1

2)

$1.5 {}^{ log_{1.5}(6) } - 3 = 6 - 3 = 3$

3)

$log_{4}(x - 5) = log_{25}(5) , \: x > 5 \\ log_{4}(x - 5) = \frac{1}{2} log_{5}(5) \\ log_{4}( x- 5) = \frac{1}{2} \\ x - 5 = {4}^{ \frac{1}{2} } \\ x = 2 + 5 \\ x = 7$

4)

$y = log_{0.1}(0.01 - {x}^{2} ) \\ D(y): \: 0.01 - {x}^{2} > 0 \\ {x}^{2} - 0.01 < 0 \\ (x - 0.1)(x + 0.1) < 0 \\ x \in ( - 0.1;0.1)$

5)

$log_{2}(16b), \: log_{2}(b) = 3 \\ log_{2}(16b) = log_{2}(16) + log_{2}(b) = log_{2}( {2}^{4} ) + 3 = \\ = 4 + 3 = 7$

6)

$log_{1.25}(0.8x + 0.4) \leqslant - 1, \: x > - 0.5 \\ 0.8x + 0.4 \leqslant {1.25}^{ - 1} \\ 0.8x + 0.4 \leqslant \frac{100}{125} \\ 0.8x + 0.4 \leqslant 0.8 \\ 0.8x \leqslant 0.4 \\ x \leqslant \frac{1}{2} \\ x \in ( - 0.5;0.5]$

7)

$log_{1.3}(5) = \frac{1}{ log_{5}( \frac{13}{10} ) } = \frac{1}{ log_{5}( \frac{1}{5} \times \frac{13}{2} ) } = \frac{1}{ log_{5}( \frac{13}{2} ) - 1 } ≈\\ ≈ \frac{1}{1.16 - 1} = \frac{1}{0.163} = \frac{100}{163} ≈6.13 \\ log_{1.3}(5) ≈6.13$