1. Solve 3=log8+3logx

2. Solve 2logx-log4=0

To solve the given equations, we'll use logarithm properties and algebraic manipulation. Let's solve them step by step.

1. Solve 3 = log8 + 3logx:

Step 1: Apply the logarithmic property log(a) + log(b) = log(ab)
3 = log8 + log(x^3)
Step 2: Apply the logarithmic property log(a^b) = b * log(a)
3 = log(8 * x^3)
Step 3: Apply the logarithmic property log(a*b) = log(a) + log(b)
3 = log(8x^3)

Step 4: Convert the logarithmic equation into an exponential equation:
10^3 = 8x^3
1000 = 8x^3

Step 5: Solve for x:
Divide both sides by 8 to isolate x^3:
125 = x^3

Step 6: Take the cube root of both sides to solve for x:
x = ∛(125)
x = 5

Therefore, the solution to the equation 3 = log8 + 3logx is x = 5.

2. Solve 2logx - log4 = 0:

Step 1: Apply the logarithmic property log(a) - log(b) = log(a/b)
2log(x) = log(4)

Step 2: Apply the logarithmic property log(a) = b is equivalent to a = 10^b
x^2 = 4

Step 3: Take the square root of both sides to solve for x:
x = √(4)
x = ±2

Therefore, the solutions to the equation 2logx - log4 = 0 are x = 2 and x = -2.