log2 16 Evaluate 2 log6 7776 middpoint log2 729 log6 8 log6

log_2 16 Evaluate 2 log_6 7776 middpoint log_2 729 log_6 8 + log_6 (1 - 4x) = log_6 63 log_6 (x - 6) + log_6 (x - 5) = 1 log_2 3x - log_2 5 = 4 log_2 9 + log_2 x^2 = 4

Solution

11) Use the log property: loga^x = x*loga

log2(16) = log16/log2 = log2^4/log2 = 4*log2/log2 = 4

12) Its blurred

13) log6(8) +log6(1-4x) = log6(63)

use the log property : logA +logB = log(A/B)

log6(8(1-4x) = log6(63)

equate the argument on both sides:

8(1-4x) = 63

8 -32x = 63

32x = -55

x = -55/32

14 ) log6(x-6) + log6(x-5) =1

use the log property : logA +logB = log(A*B)

log6(x-6)(x-5) =1

(x-6)(x-5) = 6^1

x^2 -11x +30 =6

x^2 -11x +24 =0

x^2 -8x -3x +24 =0

x(x-8) -3(x-8) =0

(x-3)(x -8) =0

x = 3 , 8

15) log2(3x) - log2(5) =4

Use the log property: logA - logB = log(A/B)

log2(3x/5) = 4

3x/5 = 2^4

3x= 16*5

x = 80/3

16 ) log2(9) +log2(x^2) =4

log2(9x^2) = 4

use the log property : logA +logB = log(A*B)

9x^2 = 2^4

9x^2 = 16

x^2 = 16/9

x = sqrt(16/9) = 4/3