1) log_3 (30x+18) - log_3 (6) = log_3 (31) 2) ln4+ln (x-7) = ln8 3) 1 / (4x-1) = 5 4) 6*4^ (log_4 (x)) = 12x-15 5) lg (5x+11) - lg1/2=lg13 6) log_1/5 (4x+7) + log_1/5 (4) = log_1/5 (24) 7) 7*7^ (log_7 (x)) = 12x-17 8) (x+2) ^5=32

1) log3 (30 * x + 18) - log3 (6) = log3 (31).

log3 ((30 * x + 18) / 6) = log3 (31).

(30 * x + 18) / 6 = 31.

5 * x + 3 = 31.

x = 28/5 = 5 3/5 = 5.6.

2) ln4 + ln (x - 7) = ln8.

L n (4 * (x - 7)) = ln8.

4 * (x - 7) = 8.

4 * x - 28 = 8.

x = 36/4 = 9.

3) 1 / (4 * x - 1) = 5.

5 * (4 * x - 1) = 1.

20 * x - 5 = 1.

x = 6/20 = 0.3.

4) 6 * 4^ (log4 (x)) = 12 * x - 15.

6 * x = 12 * x - 15.

6 * x = 15.

x = 15 / 6 = 5/2 = 2.5.

5) lg (5 * x + 11) - lg1/2 = lg13.

Lg (5 * x + 11) / (1/2) = lg13.

(5 * x + 11) * 2 = 13.

10 * x + 22 = 13.

x = - 9 / 10 = - 0. 9.

6) log1/5 (4 * x + 7) + log1/5 (4) = log1/5 (24).

log1/5 ((4 * x + 7) * 4) = log1/5 (24).

(4 * x + 7) * 4 = 24.

16 * x + 28 = 24.

16 * x = - 4.

x = - 4/16 = - ¼ = - 0.25.

7) 7 * 7^ (log7 (x)) = 12 * x - 17.

7 * x = 12 * x - 17.

5 * x = 17.

x = 1 7 / 5 = 3 2 / 5 = 3.4.

8) (x + 2) ^5 = 32.

(x + 2) ^5 = 2 ^5.

x + 2 = 2.

x = 0.