Evaluate each expression log10 00001 log35 35 log40 110 logg

Evaluate each expression. log_10 0.0001 log_35 35 log_40 1/10 log_g 1 log_5 5 log_5 1/25 log_7 7 log_7 1 log_2 1/8 10^log_10 5 log_30 0.1 log_28 1 log_7 sqrt 7 log_6 216 log_3 81 log_2 16 log_10 (log_7 7 log_5(log_2 32) log_2 1/32 Solve each equation. log_7 x = 2 log_x 2 = 1/2 log_4 x = -3/2 log_9 x = 3/2 log_8 x = 4/3 Write each expression as a single logarithm. log_5 5/7 + log_5 40/25 log_3 3/4 - log_3 3/8 log_e (a^2 - ab) - log_e(7a - 7b) log(b^2 + b) - log(b^2 -b) log(4u^2 - 9) - log(8u^3 - 27 log_7(1/4 - 1/x^2) - log_7 (1/2 - 1/x) log_2 32/11 + log_2 121/16 - log_2 4/5 2log_8 x - 2/3 log_8 x + 4 log_8 x 5log_6 x - 3/4 log_6 x + 3 log_6 x log(3x^2 + 7x + 4) - log(3x^2 - 5x - 2 log(x^2 - 6x + 9) - log(x^2 - 6x - 9) 1/2 log_8(x - 1) - 3log_8 (x + 2)

Solution

24. log35(35) = log35/log35 =1

26. log5(1) = log1/log5 = 0

28 log5(1/25) = log5(5^-2) = -2log5/log5 = -2

30. log7(1) = log1/log7 = 0

32 .not visble

34. not visible

38.log2 (16) = log2(2^4) = 4log2/log2 = 4

40. not visible

42 log7(x) =2

use the log to exponential property : y = a^x ---> lna(y) = x

x= 7^2 =49

44. log4(x) = -3/2

use the log to exponential property : y = a^x ---> lna(y) = x

x = 4^(-3/2) = 2^(2*-3/2) = 2^-3 = 1/8