6*log1/2 32-20*log3 27+5*lg0,00001

1)

log3(27) - log(1/7)(7) = log3(3³) - log7(7)/log7(1/7) = 3log3(3) - 1/log7(7^(-1)) = 3 - 1/(-1) = 3 + 1 = 4.

2)

2^(1 + log2(5)) = 2^(log2(2) + log2(5)) = 2^log2(2 * 5) = 2^log2(10) = 10.

3)

lg4 + 2lg(5) = lg4 + lg(5²) = lg4 + lg(25) = lg(4 * 25) = lg100 = lg(10²) = 2.

4)

a)

3^x = 7;

log3(3^x) = log3(7);

xlog3(3) = log3(7);

x = log3(7).

b)

log4(x) = log0,5(√2);

log2(x)/log2(4) = log2(2^(1/2))/log2(1/2);

log2(x)/log2(2²) = (1/2)/log2(2^(-1/2));

log2(x)/2 = (1/2)/(-1/2);

log2(x)/2 = -1;

log2(x) = -2;

x = 2^(-2) = 1/4.