Determine the value of the unknown in each of the following

Determine the value of the unknown in each of the following equtions.

a. 1 + ln(2-x)=1

b. (5²⁾³ = 5^x

c. log₂(log_x(16)) = 2

d. ln(7x) = 2.4

e. ln(x+4)= 3

f. log₆(x-8) = 4

g. 2000= 20(3)^2x

a) 1 + ln(2-x) = 1 =========> ln(2-x) = 0

2-x = 1 =====> 2 - x = 1 ========> x = 1

b) (52)3 = 5x ====> x = 52*3/5 = 31.2

c) log2(logx(16)) = 2 ========> log 2 *[log x + 4*log 2] = 2

d) ln(7x) = 2.4 =======> 7x = 11.023 =========> x = 1.575

e) ln(x+4)= 3 ======> (x+4) = 20.1 =======> x + 4 = 404.01 =======> x = 400.01

f) log6(x-8) = 4 =====> log 6 + log (x-8) = 4 ======> log (x-8) = 3.222 ======> x = 33.08

g) 2000= 20(3)2x =====> x = 2000/(20*3*2) = 16.67