To solve, do the following steps:

2log5 + 3logx = 2

-> log5^2 + logx^3 = 2

-> = log25*x^3 = 2

-> 25*x^3 = 10^2

-> 25*x^3 = 100

-> Divide by 25

-> x^3 = 4

-> Take the cube root

->** x = (4)^(1/3)**

To solve for x in 2log5 +3logx =2

Solution:

2log5 = log 5^2 =log25, as n*log b = logb^n

3logx = logx^3

and 2 = lof10^2 = log 100.

Replacin in the given equation:

log25*logx^3 = log 100.

log(25x^3) = log 100. Taking antilogarithms,

25x^3 = 100

x^3 = 100/25 = 4

x^3 = 4. Take the cube root.

x = 4^(1/3) is the real solution.

First, we'll use the power property of logarithms, for the terms of the expression:

2 log 5 = log 5^2

3 log x = log x^3

2 log 5 + 3 log x = log 5^2 + log x^3

Now, we'll use the product property of logarithms:

log 5^2 + log x^3 = log 25*x^3

log 25*x^3 = 2

25*x^3 = 10^2

25*x^3 = 100

We'll divide by 25 both sides:

x^3 = 4

**x = 4^(1/3)**

The equation 2log5 + 3logx = 2 has to be solved for x.

The problem is being solved with logarithm to base 10.

2log5 + 3logx = 2

Use the property of logarithm, log a + log b = log a*b and a*log b = log b^a

log 5^2 + log x^3 = 2

log 25*x^3 = 2

25*x^3 = 10^2

x^3 = 4

x = 4^(1/3)

The solution of the equation 2log5 + 3logx = 2 is x = 4^(1/3)