Logarithm help, please and thank you?

Question

Here are some problems I'm having help with:
1. Use natural logarithms to solve each equation or inequality.
a. 24 b. 15e^x>200

2. Solve each equation
a. log base x of 81=4.
b. log base 2 of x=1/3 log base 2 of 27

3. solve each equation or inequality
a. 4^x=6^(x+2)
b.(1/4)^3x<6^(x-2)

Answer 1

(1a)
ln 24 < 2x
2x > ln 24
x > ln 24/2

(1b)
15x > ln 200
x > ln 200/15

(2a)
x^4 = 81
x = 3

(2b)
x^3 = 27
x = 3

(3a)
x log 4 = (x+2) log 6
x log 4 = x log 6 + 2 log 6
x log 4 - x log 6 = 2 log 6
x(log 4 - log 6) = 2 log 6
x = (2 log 6) / (log 4 - log 6)

(3b)
3x log 1/4 < (x-2) log 6
3x log 1/4 < x log 6 - 2 log 6
3x log 1/4 - x log 6 < -2 log 6
x (3 log 1/4 - log 6) < -2 log 6
x < (-2 log 6) / (3 log 1/4 - log 6)

Answer 2

2x > ln 24; x > 1.59
x > ln 200/15 > 2.59

x^4 = 81; x = 3
x = 27^1/3, x= 3

solve this using a calc,
xlog4 = (x+2)log6
3xlog(1/4)<(x-2)log6

Answer 3

i know only second one
a) log base x of 81=4
powerof x be 4=81
x=3*3*3*3
x=3 ans

b) x=3ans