what are the answers to the following;?

Question

2 exponent 3x =4

and
5 over 6x = 10?

Answer 1

Problem #1:
2^(3x) = 4

Since you have powers of 2, I would take the log base 2 of both sides:
log[2](2^(3x)) = log[2](2²)
3x = log[2](2²)
3x = 2
x = 2/3

Problem #2:
5/6x = 10

Multiply both sides by x
5/6 = 10x

Divide both sides by 10:
5/60 = x

Reduce:
x = 1/12

Your answers are:
2/3 and 1/12

Answer 2

2^3x=2^2
comparing the powers
3x=2
dividing by 3
x=2/3

2.5/6x=10
x-multiplying
60x=5
dividing by 60
x=5/60
=1/12

Answer 3

2^3x=4
3x ln 2=2 ln 2 divide by ln 2
3x=2 divide by 3
x=2/3

5/6x=10 multiply bu x
5/6=10x divide by 10
5/60=x
x=1/12